Masters Thesis

Computer Simulation of a 3D, 3 Link, Diver with Cross Product Driven PD Control

By Richard Nicholas Bomba

Submitted in Partial Fulfillment of the Requirements for the Degree Master of Science

Supervised by Professor Roger F. Gans

Department of Mechanical Engineering Arts, Sciences, and Engineering School of Engineering and Applied Sciences

University of Rochester Rochester, New York

2008

2 Curriculum Vitae

The author was born in Rochester, NY on July 15, 1984.

He attended Rensselear

Polytechnic Institute in Troy, NY from 2002 to 2005 when he graduated with a Bachelor of Science in mechanical engineering. He came to the University of Rochester in the fall of 2006 and began studies in mechanical engineering.

He pursued his research in

dynamics and control under the direction of Professor Roger F. Gans and received the Master of Science degree from the University of Rochester in 2008.

3 Acknowledgements

I would like express my gratitude and thanks to Professor Roger F. Gans for his guidance and instruction throughout the course of my research.

His insight and constructive

criticism was always invaluable to my work.

I would also like to thank the staff and faculty of the Mechanical Engineering department for their instruction and support during my time at the University of Rochester. Their efforts directly contributed to this accomplishment.

Finally, and most importantly, I would like to thank my family and friends for their interest, support, and patience for the duration of the process. This would especially not be possible without my parents which always enabled me to focus my main efforts on my work.

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Table of Contents Table of Contents ............................................................................................................4 List of Tables & Figures ..................................................................................................6 Abstract ...........................................................................................................................8 1. Introduction .................................................................................................................9 Thesis Statements ........................................................................................................9 Previous Research......................................................................................................10 Motion Capture......................................................................................................10 Direct Analysis ......................................................................................................13 Numerical Methods................................................................................................15 Miscellaneous ........................................................................................................16 System Description....................................................................................................17 Model Uniqueness .....................................................................................................18 Plan of Action............................................................................................................19 2. Formulation ...............................................................................................................20 Model Construction ...................................................................................................20 Coordinate Systems ...............................................................................................20 System Energies and Generalized Coordinates.......................................................22 Kinematic Constraints – Position Vectors ..............................................................23 Kinematic Constraints – Velocity Vectors..............................................................23 Body Axis Angular Velocities................................................................................24 Generalized Forces ................................................................................................24 Equations of Motion ..............................................................................................28 Conversion to State Space......................................................................................28 Data Manipulation .....................................................................................................31 System Center of Mass ..........................................................................................31 Linear and Angular Momentum .............................................................................32 Uncontrolled Test Simulations...................................................................................34 Simulation Overview .............................................................................................35 Case 1 – Simple Free Fall ......................................................................................35 Case 2 – Helix .......................................................................................................39 Case 3 – Irregular Initial Conditions & Conservation of Momentum ......................42 3. Control ......................................................................................................................47 Desired States............................................................................................................47 Gain Selection ...........................................................................................................48 Physical Interpretation ...............................................................................................49 Controlled Test Cases – Overview .............................................................................51 Case 1 – Straightening of a 3D Initial Configuration ..................................................52 Case 2 – Resistance of Initial Angular Velocities in 2 Links ......................................57

5 Case 3 – 2D Non-collinear Desired State ...................................................................63 4. Simulations................................................................................................................69 Case 1 – System Configuration & Rotational Inertia ..................................................72 Case 2 – Generating Twist .........................................................................................81 5. Discussion and Conclusions.......................................................................................88 Results Summary.......................................................................................................88 Future Work ..............................................................................................................91 Appendix A – Algebraic Derivation using Maple 10......................................................93 Variable Definitions...................................................................................................93 Table A1. Variables for the Equations of Motion ..................................................93 Table A2. Variables for the Generalized Forces ....................................................94 Table A3. Variables for the Coefficient Constants.................................................94 Table A4. Variables for the Data Manipulations....................................................95 Maple 10 Worksheets ................................................................................................95 Equations of Motion ..............................................................................................95 Generalized Forces ................................................................................................98 Coefficient Constants...........................................................................................101 Data Manipulations..............................................................................................105 Appendix B – MATLAB Numerical Model .................................................................110 Table B1. MATLAB Numerical Model Quick Reference........................................110 Main Routine – Main.m ...........................................................................................110 Initial Conditions – ICS.m .......................................................................................112 Physical Parameters – Constants.m ..........................................................................113 System in State Space Form – SYS.m......................................................................114 Coefficient Constants - Cs.m ..................................................................................118 Control Torques – Ts.m ...........................................................................................169 Coefficient Constants in ‘for loop’ Form – Csi.m.....................................................191 Rotation Matrices – Rotations.m..............................................................................246 COM Kinematics – COM.m ....................................................................................249 Generalized Coordinate Accelerations – TT.m.........................................................250 Body Axis Angular Velocities – Omega.m ..............................................................254 Control Effort, Cross Products, & Joint Angles – Controls.m...................................255 Linear & Angular Momentum Calculations – Momentum.m....................................264 Plot Generation – Plots.m ........................................................................................283 Appendix C – Main Routines for Cases 1 and 2 ...........................................................294 Case 1 – Main.m......................................................................................................294 Case 2 – Main.m......................................................................................................296 Works Cited ................................................................................................................298

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List of Tables & Figures Figure 1.1: General System Representation...................................................................17 Figure 2.1: Coordinate Systems ....................................................................................21 Figure 2.2: Example System .........................................................................................30 Table 2.1: Physical Parameters .....................................................................................35 Table 2.2: Gains ...........................................................................................................35 Figure 2.3: Case 1 Expected Results ..............................................................................36 Table 2.3: Case 1 Initial Conditions ..............................................................................36 Figure Set 2.4a: Case 1 Results......................................................................................37 Figure Set 2.4b: Case 1 Results......................................................................................38 Table 2.4: Case 2 Initial Conditions ..............................................................................39 Figure 2.5: Case 2 Initial Configuration .........................................................................40 Figure Set 2.6a: Case 2 Results......................................................................................40 Figure Set 2.6b: Case 2 Results......................................................................................41 Table 2.5: Case 3 Initial Conditions ..............................................................................43 Figure Set 2.7a: Case 3 Results......................................................................................43 Figure Set 2.7b: Case 3 Results......................................................................................44 Figure Set 2.7c: Case 3 Results......................................................................................45 Figure 3.1: Analogous Configurations ..........................................................................47 Figure 3.2: Motor Driven Ball Joint Concept ................................................................50 Table 3.1: Physical Parameters .....................................................................................51 Table 3.2: Gains ...........................................................................................................52 Table 3.3: Case 1 Initial Conditions ..............................................................................52 Figure 3.3: Case 1 Initial Configuration .........................................................................53 Figure Set 3.4a: Case 1 Results......................................................................................54 Figure Set 3.4b: Case 1 Results......................................................................................55 Figure Set 3.4c: Case 1 Results......................................................................................56 Table 3.4: Case 2 Initial Conditions ..............................................................................58 Figure 3.5: Case 2 Initial Configuration .........................................................................58 Figure Set 3.6a: Case 2 Results......................................................................................59 Figure Set 3.6b: Case 2 Results......................................................................................60 Figure Set 3.6c: Case 2 Results......................................................................................61 Table 3.5: Case 2 Initial Conditions ..............................................................................63 Figure 3.7: Case 3 Desired State ...................................................................................64 Figure Set 3.8a: Case 3 Results......................................................................................65 Figure Set 3.8b: Case 3 Results......................................................................................66 Figure Set 3.8c: Case 3 Results......................................................................................67 Figure 4.1a: System Pre-Twist Maneuver ......................................................................70 Figure 4.1b: System Post-Twist Maneuver.....................................................................71 Table 4.1: Case 1 Physical Parameters ...........................................................................73 Figure 4.2: Case 1 Desired States...................................................................................73

7 Table 4.2: Case 1 Initial Conditions ..............................................................................74 Table 4.3: Case 1 Segment I Gains ...............................................................................74 Table 4.4: Case 1 Segment II Gains ..............................................................................75 Table 4.5: Case 1 Segment III Gains .............................................................................75 Figure Set 4.3a: Case 1 Results......................................................................................76 Figure Set 4.3b: Case 1 Results......................................................................................77 Figure Set 4.3c: Case 1 Results......................................................................................78 Figure Set 4.3d: Case 1 Results......................................................................................79 Figure 4.4: Case 1 General Results ................................................................................80 Table 4.6: Case 2 Initial Conditions ..............................................................................82 Table 4.7: Case 2 Gains ................................................................................................82 Figure 4.5: Case 2 Desired States...................................................................................83 Figure Set 4.6a: Case 2 Results.....................................................................................84 Figure Set 4.6b: Case 2 Results.....................................................................................85 Figure Set 4.6c: Case 2 Results.....................................................................................86

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Abstract This document presents a three-dimensional (3D) mathematical model for the dynamical behavior of three rigid links joined end to end by “ideal” joints. The joints allow unrestricted relative rotation while restricting relative translation. Proportional-derivative (PD) control torque, driven by the cross products between adjacent links, controls the mid-flight configuration of the system. The intention of the model is to mimic the maneuver of a diver (or gymnast, . . .) during the free-fall phase of a dive. The equations of motion are the usual Euler-Lagrange equations converted to state space form for numerical integration, which uses a unique technique to reduce the length of the code and the number of floating point operations. Test calculations verify the model for some simple cases, both with and without control torques. The control scheme is able to mimic various planar diving maneuvers. The system presented here is not capable of more complex full three-dimensional dives. Extension seems possible, and will be discussed.

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1. Introduction This document investigates the behavior of a series of linked rigid bodies in free fall with zero external torque about the systems center of mass (COM). This means that angular momentum about the system’s COM must be conserved. Real-life examples of this class of system include aerial divers and gymnasts, freestyle skiers, and cats attempting to land on their feet. These examples are able to manipulate their rotational inertia by changing their body configuration. This enables them to better take advantage of their angular momentum to perform a desired maneuver, such as a somersault. The system considered here is comprised of 3 rigid links joined end to end. A more detailed description is offered later, but this system can be used to study the type of movements seen in the above examples.

Thesis Statements This document is written with the intention of validating three main statements. First, the Euler-Lagrange equations of motion provide a valid model for the numerical integration of (3D) chain dynamics problems when converted to state space (SS) form using the unique method outlined in this document. Second, a three link chain dynamics model with joints allowing unrestricted rotation and cross product driven linear PD controls is able to accurately mimic many diving motions, but not all. In addition, it provides the opportunity to study the dynamics of additional free fall motions. Thirdly, this model provides a starting place for future studies in 3D chain dynamics and modeling of acrobatic maneuvers.

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Previous Research Analysis of diving (and gymnastics and related maneuvers) has been approached using two different methods. The first approach observes and collects data on the kinematics of the actual maneuver and then builds a model to better understand the kinetics. This approach is often referred to as motion capture. The second approach is to create a theoretical model which is able to model the dynamics without relying on kinematic input. This approach will be referred to as direct analysis. Other relevant work covers research done on the numerical methods used to integrate complex systems written in state space form. There are also papers dealing with variable inertia in other contexts. They can be found in the miscellaneous section below.

Motion Capture There are two ways to gather the kinematic data used in motion capture. The first one is easier and cheaper, but prone to more error. It involves analyzing a video frame by frame of an athlete performing a given maneuver.

The researcher then can then make

reasonable estimations of joint angle, angular velocity, and muscle activation timing (the point in the maneuver in which the athlete begins to change his body’s configuration). The second method is far more cumbersome, but produces accurate and automated results. Data are obtained by tracking reflective sensors on the subject by a series of cameras positioned at different angles. These data are then interpreted using computer software, unique to each application, to extrapolate a range of kinematical data.

King and Yeadon1 used a 2D, five segment, model when they investigated the variables affecting the number of somersaults a leaping gymnast can perform. The model was

11 subjected to several different initial conditions (take off angle and velocity, angular momentum, and body configuration).

The results were compared to video data of

gymnast performing the same movement with the goal finding the most efficient set of initial conditions.

Hiley and Yeadon2 use a previous model3 to investigate the feasibility of the triple somersault dismount maneuver from the high bar in Olympic gymnastics which at the time of the article had yet to be performed. They used motion capture data to determine the initial conditions for the dismount from the bar and the model numerically computes the flight of the gymnast. They find the maneuver to be possible for appropriate initial conditions.

King and Yeadon4 also use a five segment planar model representing the feet, shanks, trunks, torso, and head to compare the timing in the maneuvers for a single and double somersault. Video data of gymnasts performing the maneuvers is also used to determine the initial angular momentum at take off.

King, Yeadon, and Wilson5 also investigate the joint angular velocity and torque generation at the knee joint using movement data and a dynamometer. Even though no free fall is modeled, the value of this article lies in understanding the shape and magnitude of torques controlling the knee. The results show a steep slope at initial activation followed by a far shallower slope as the goal is approached.

12 Yeadon, King, and Kong6 use a planar computer model, created by a commercial software package (Autolev 3.4TM) to simulate the take off from a spring board. The goal of this model is to be able to generate an estimation of the joint activation torques for a specific subject based on their take off and subsequent aerial maneuver. Movement data from an elite gymnast is provided as a basis for comparison.

Yeadon also published the following series of articles on the process of obtaining and constructing simulations with movement data. The first article7 shows how to work out the geometry associated with obtaining information frame by frame from video data. The second article8 shows how to develop a mathematical model for the inertia of the human body by dividing it into 3D rigid segments. It also provides a method for determining the location of the body’s COM. The third article9 shows how to determine the angular momentum of the system modeled in the second article. Finally, the fourth article10 presents a mathematical computer model which can be used along with appropriate initial conditions and motion data to solve for the motion of the human body.

Cheng and Hubbard11 use a four segment planar human model (feet, shanks, thighs, and torso) to study the optimal take off motion from a compliant surface such as a spring board. The model contains joint angle and angular velocity dependent torques which were limited to the capabilities of a human subject. The mathematical model is used to estimate the maximum height of the jump given input of the pre take off routine obtained from film data. The model is able to utilize the joint torques to make a more efficient use of the energy stored in the spring board and achieve a higher jump height.

13

Blajer and Czaplicki12 use a nine segment planar human model to study the joint torque an athlete experiences while performing a somersault on trampoline. Motion capture is used to obtain the kinematics of each segment in the model. Inverse dynamics is used to interpret this data and calculate the torque at the joints. A spring and damper based model for the trampoline is also provided.

Mathiyakom, McNitt-Gray, and Wilcox13 use the motion capture of thirteen sensors attached to the subject’s body to study the difference in the jumps produced by rocking forward into the jump and a normal standing start. A commercial package (C2S NAC Visual Systems) produced the kinematics of the motion. Inverse dynamics was then used to study the joint torques.

Griffiths, Watkins, and Sharpe14 present the documentation for a mechanical apparatus which is able to determine experimentally the moment of inertia about a variety of axes. The apparatus is constructed from a freely rotating turntable attached to a fixed falling mass. The resulting angular velocity is measured using video motion capture. Friction is accounted for in the data manipulation.

Direct Analysis Springings and Yeadon15 use a 2D model, comprised of two segments, to investigate somersaults performed during a Hecht vault. The dynamics of the model are built using a vector based Newtonian approach. The main goal of this work is study the role in which

14 pre-vault trajectory plays in the athlete’s ability to reverse his or her direction of rotation. It was found that a proper trajectory is able to produce up to half of the change in direction alone.

Frolich16 investigates how an athlete is able to rotate during free-fall if the angular momentum of the system is zero. Many divers and gymnasts are able to perform limited maneuvers by “winding up” their body. Frolich uses simple models built using vector dynamics to show that vector sum of the angular momentum remains zero throughout the entirety of these maneuvers. For example, generating a positive angular velocity in the legs will produce an opposite angular velocity in the torso in order to offset the angular momentum generated by the legs. Edwards17 also investigates this scenario using two very simple cases. The first one models a three segment dancer attempting to rotate about the long axes of the human body by scissoring his or her legs. The second one models a cat righting itself during a fall in order to land on its feet. It is comprised of two cylinders joined end-to- end at a joint which allows relative rotation and tilt between them. Using these models, Edwards similarly shows that the vector sum of the angular momentum remains zero during the maneuver.

Iwai18 discusses many of the methods used in multibody dynamics, including the Lagrange Equations, the Hamiltonian, COM calculations, and constraints. After the general description, Iwai builds a model very similar to Edwards’19 falling cat model. The main difference is that Iwai develops the equations of motion using the Lagrange

15 technique. Simulation results show that the same maneuver can be completed with the total angular momentum remaining zero.

Wooten and Hodgins20 provide the most complete and anatomically correct simulation of human diving. A 3D, computer rendered, model with 15 rigid segments and 32 actuated degrees of freedom is used to model a human diver performing several different maneuvers. The equations of motion, including takeoff and free fall, are generated using a commercial package (SD/FAST) which uses an automated variation of Kane’s method. The torque at each of the joints is inserted as (PD) torque which is a function of the joint angle. Gains are empirically chosen. Also, motion capture data is obtained of a diver performing each of the maneuvers. From the motion capture data, the timing of each maneuver and body joint angles is obtained. The results of these simulations were able to match the human diver very well.

Numerical Methods Kane and Levinson21 compare the efficiency of numerical simulations for the Lagrange, Newton-Euler, and Kane equations of motion of the Stanford robotic arm (six degrees of freedom). Kane shows that his equations of motion are the most efficient. During the derivation of the equations of motion, Kane collapses long expressions into single coefficients which greatly reduce the number of calculations during simulation.

A

technique similar to this is an integral part of the numerical simulation this document. It will be described below.

The heart of the idea is to replace a small number of

complicated differential equations with a large number of simple differential and algebraic equations.

16

Ren and Zheng22 present a method to decouple nonclassical linear systems already written in the state space form. The goal is to write the state matrix into upper triangle form where the last state variable can be solved for explicitly before finding the others one at a time using back substitution. The technique described in the article is called the Real Schur Decomposition. A numerical model based on a simple torsion model is presented.

Miscellaneous Costello and Frost23 research using an unbalanced mass mounted inside an artillery shell to make small corrections in its trajectory. The unbalanced mass is mounted on a shaft connecting the point and the rear of the shell. A servo motor driven by an unspecified feedback driven control rotates the mass. The change in inertia is able to change the angle of attack of the shell which changes its aerodynamic properties and subsequently its trajectory.

Gans24 investigates chain dynamics by modeling a conservative elastic pendulum as a series of rigid links connected with torsion springs at their joints. The equations of motion are generated using the Lagrange technique and are used to investigate windows of periodic behavior in the dynamic response of a 2D, four element, inverted pendulum model.

Edelstein and Rosen25 develop the general 3D system dynamics for a series of chained links anchored at one end. This model accounts for the elastic deformations in the

17 individual links. It also models different types of joints as rigid bodies giving them a finite mass.

The equations of motion are developed using a modified Lagrangian

approach and the results of numerical simulations are presented.

System Description The system being considered contains three uniform rigid links connected end to end by two joints.

The joints constrain all three translational directions of relative motion

between the links, but allow for complete freedom for all three relative rotations. Torque has been inserted at the joints to produce rotation between the links with the intention of altering the systems configuration mid-flight. They are modeled to add no external work to the system thus conserving angular momentum. Figure 1.1 shows a general 3D model of the system:

Figure 1.1: General System Representation The above system can easily be customized by choosing the three masses and the three lengths along the principle axes of each link.

This introduces nine total principal

moments of inertia. Air resistance is assumed to be negligible. The joints are assumed to be ideal, thus having no mass, volume or friction. This model concerns free-fall of the assembly only and assumes that all the necessary initial conditions are known.

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Model Uniqueness There are three main areas which this model differentiates itself from previous work. The first area is the method used to convert the Euler-Lagrange equations of motion into state space. Due to the nature of the kinematics in the problem, this is necessary before numerical integration can be performed. The method involves taking advantage of the quasi-linear form of the equations of motion and replaces long coefficients with a single place holder variable while performing standard linear algebra techniques. The result is to connect the complicated 24 dimensional state equations to a much smaller 78 dimensional differential-algebraic system. The idea comes from Kane & Levinson21, but its application to the Euler-Lagrange system appears new.

The second unique area is the selection of a 3D model with complete freedom of rotation in the joints. Previous models were built limiting the range of motion and degrees of freedom either by using a planar 2D model or a 3D model with limited range of motion. The current model allows greater flexibility in the types of motion which can be studied, and can be restructured as necessary to model specific anthropomorphic motions.

The third unique area is the use of cross product driven PD control torque to alter the configuration of the system. Most free-fall models take advantage of restricted degrees of freedom in joints and are able to apply simple linear PD control torques. This does not work well with the extended joint freedom of the model proposed. The combination of linear control theory and the nonlinear cross product provide a solution capable of

19 controlling the system to a large class of desired states. Further work is necessary to extend the range of control.

Plan of Action The following sections of this document aim to accomplish the following seven goals: 1. Comprehensive development of the Euler-Lagrange equations of motion and demonstration of how they can be put in state space suitable for numerical integration. 2. Provide simple uncontrolled test cases to both assist in understanding of the model and provide model validity. 3. Develop a PD Control which is able to control the value of the cross product between the body axes of connected links. 4. Provide simple test cases to demonstrate both the behavior of the control and the effect manipulating the system’s configuration has on its free fall behavior. 5. Demonstrate the model’s ability to obtain analogous forms of three major diving positions and use it to understand how these positions are related to the system’s moments of inertia. 6. Exhibit the model’s short-coming in its failure to adequately produce a twisting motion by completing a maneuver analogous to the type competitive divers perform. 7. Offer suspected reasons for failure and provide suggestions for future models.

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2. Formulation Model Construction This section describes the development of the Euler-Lagrange equations of motion and demonstrates a method for converting them into a state space form suitable for numerical integration in complex systems.

Coordinate Systems The system in this document can be described by four coordinate systems. In each system x, y, z denote Cartesian coordinates and i, j, k , their corresponding unit vectors. The first coordinate system is fixed in an inertial space, referred to as the spatial frame, and written in upper case. The next three coordinate systems (lower case) are body fixed with the origin at the center of mass (COM) and axes aligned with the principal axes of inertia. These rotate and translate with the body. A representation of the system and corresponding coordinate axes can be seen below:

21

Figure 2.1: Coordinate Systems

(a) (r1 , r2 , r3 ) Denote vectors from the origin to the COM of individual bodies. (b) Typical body coordinate system.

The body coordinate systems are each related to the spatial frame by three translational components (r1 , r2 , r3 ) and three Euler angles26. When r2 and φ 2,θ 2,ψ 2 are zero the frames are coincident.

Formal rotations between the spatial and body systems (all

coordinates being implicit functions of time) are given below:

22

 cos( φ ) sin( φ ) 0 R( φ ) = − sin( φ ) cos( φ ) 0  0 0 1 0 0  1   R( θ ) = 0 cos( θ ) sin( θ )    0 − sin( θ ) cos( θ )

(2.1)

 cos(ψ ) sin(ψ ) 0 R(ψ ) = − sin(ψ ) cos(ψ ) 0  0 0 1 The rotation from spatial coordinates to body coordinates is then:

x = R (ψ ) ⋅ R (θ ) ⋅ R (φ ) ⋅ X R i = R (ψ ) ⋅ R (θ ) ⋅ R (φ )

(2.2)

i = 1..3

These are proper rotations so transforming body coordinates to spatial coordinates is done with the transpose of the rotation.

System Energies and Generalized Coordinates The general (unconstrained) kinetic and potential energies (T and V respectively) of this system are shown in equations 2.3 (an overhead dot denotes derivative with respect to time): 3 1 1 T = ∑  m n x& n2 + y& n2 + z& n2 + J x ω x2 2 n =1  2

(

V = ∑ [mn gz n ]

)

(

)

n

+

(

1 J y ω y2 2

3

)

n

+

1  J z ω z2 n  2 

(

)

(2.3)

n =1

Equation 2.3 shows eighteen dependent variables, twelve of which are independent and cannot be explicitly expressed using the other variables.

These other six are not

independent because the bodies are connected. The COM coordinates of the middle body

23

( x2 , y 2 , z 2 ) were chosen for the

sake of symmetry to reduce the number of generalized

coordinates to twelve: nine Euler angles and the three selected position coordinates.

q = {x 2 , y 2 , z 2 , φ1 , θ 1 ,ψ 1 , φ 2 , θ 2 ,ψ 2 ,φ 3 , θ 3 ,ψ 3 }

T

{

q& = x& 2 , y& 2 , z& 2 , φ&1 , θ&1 ,ψ& 1 , φ&2 , θ&2 ,ψ& 2 ,φ&3 , θ&3 ,ψ& 3

}

T

(2.4)

Kinematic Constraints – Position Vectors The kinematic constraints that eliminate r1 and r3 can be most easily described with reference to Figure 2.1(a). The upper end of the first body must be coincident with the lower end of the second body, and the upper end of the second body must be coincident with the lower end of the third body. These can be written using the transpose of the transformations written in equation 2.2.

 x2    r1 =  y 2  − R T2 z   2  x2    r2 =  y 2  z   2

0   ⋅  0  − R 1T c   2

0    ⋅ 0  c   1 (2.5)

 x2    r3 =  y 2  + R T2 z   2

0   ⋅  0  + R T3 c   2

0   ⋅0 c   3

Kinematic Constraints – Velocity Vectors One can find the velocities that enter into the kinetic energy expression by differentiating the position vectors, remembering that the rotation matrices’ are functions of time.

& = d R (t ) R i i dt From equation 2.5 the velocity vectors are shown below:

(2.6)

24

 x& 2    &T r&1 =  y& 2  − R 2  z&   2

 x& 2    r&2 =  y& 2   z&   2

0   &T ⋅0−R 1 c   2

0    ⋅ 0  c   1 (2.7)

 x& 2    &T r&3 =  y& 2  + R 2  z&   2

0   &T ⋅0+ R 3 c   2

0   ⋅0 c   3

Body Axis Angular Velocities Equation 2.3 expresses the rotational terms in the kinetic energy as functions of the body axis angular velocities. Kinetic energy is a scalar so this choice of axes may be made for convenience. These angular velocities are functions of both the Euler angles and their rates of change and can be rewritten entirely in terms of the generalized coordinates as follows27:

(ω x )i

(ω )

y i

(ω z )i

= φ&i sin(θ i ) sin(ψ i ) + θ&i cos(ψ i ) = φ& sin(θ ) cos(ψ ) − θ& sin(ψ ) i

i

i

i

i

i = 1..3

(2.8)

= φ&i cos(θ i ) + ψ& i

Generalized Forces Control of the system’s configuration can be accomplished by applying torque at each of the system’s two joints. Each torque has three components that can be written about any set of Cartesian axes. They are expressed in the inertial frame during the derivation of the equations of motion.

The magnitude of each torque component is determined using a

(PD) control that controls the value of the cross product between the two adjoining links.

25 The method chosen to quantify the relationship between two joined links was the cross product between the corresponding body z axes. The z axis was the logical choice because it is the axis the links are connected along. Shown below are the cross products and their time derivatives with the subscript notation 21 referring to link 2 with respect to link 1:

r z 21

r z 32

  =  R 1T  

  =  R T2  

0      ⋅ 0  ×  R T2 1     

0       ⋅ 0  ×  R T3 1     

0    ⋅ 0  1    

0    ⋅ 0  1   

v z 21 =

d r z 21 dt (2.9)

v z 32 =

d r z 32 dt

After evaluation, equation 2.9 is a vector of constants. The PD control is designed to drive this value to a null vector unless a desired state is specified.

The desired state

vector is seen below with dij representing scalar components:

rd z 21

rd z 32

d 11    = d 12  d   13 

d 31    = d 32  d   33 

vd z 21 =

d rd z 21 = 0 dt (2.10)

vd z 32 =

d rd z 32 = 0 dt

Equations 2.9-10 can be used along with proportional gains (KZ ) and velocity gains

( JZ )

to form the following PD control which drives the cross product to the desired

vector rd z .

τ z 21 = KZ 21 (r z 21 − rd z 21 ) + JZ 21v z 21

τ z 32 = KZ 32 (r z 32 − rd z 32 ) + JZ 32 v z 32

(2.11)

26 The cross products in equations 2.11 have one major disadvantage. They are unable control any rotation about the z body axes once the system straightens out. In numerical testing it was found that straightening the rods would often lead to unchecked equal and opposite accelerations about body z axis. In order to combat this, a second and third (only one is used depending on the movement) PD control was built using the cross product between the x and y axes of connected bodies. The x axis cross product is seen below:

r x 21

r x 32

  =  R 1T  

  =  R T2  

1      ⋅ 0  ×  R T2 0     

1      ⋅ 0  ×  R T3 0     

1    ⋅ 0  0   

1    ⋅ 0  0   

v x 21 =

d r x 21 dt

(2.12) v x 32 =

d r x 32 dt

The desired state of this control is a cross product with all zero components meaning the torque is written as follows:

τ x 21 = KX 21 r x 21 + JX 21 v x 21

(2.13)

τ x 32 = KX 32 r x 32 + JX 32 v x 32 Similarly for the y axis:

r y 21

r y 32

  =  R 1T  

  =  R T2  

0      ⋅ 1  ×  R T2 0     

0      ⋅ 1  ×  R T3 0     

0    ⋅ 1  0   

0    ⋅ 1  0   

v y 21 =

d r y 21 dt

(2.14) v y 32 =

τ y 21 = KY21 r y 21 + JY21v y 21 τ y 32 = KY32 r y 32 + JY32 v y 21

d r y 32 dt

(2.15)

27

Equations 2.11, 2.13 and 2.15 can be combined to get the equations for the total torque applied at the joint.

τ 21 = τ z 21 + τ x 21 + τ y 21

(2.16)

τ 32 = τ z 32 + τ x 32 + τ y 32

The torque is inserted so it acts on the spatial axes. The virtual displacements (rotations in this case) corresponding to a body’s movement about the inertial axes as a result of an applied torque are: δφ i    T δ Ω i =  0  + R (φ )i  0   

δθ i    T T ⋅  0  + R (φ )i ⋅ R (θ )i  0   

 0    ⋅ 0  δψ   i

(2.17)

The virtual work quantifies both the magnitude of the applied torque and its direction of action. Care needs to be taken when writing the virtual work to ensure that the joint torques do not change the initial angular momentum of the system. The virtual work, a scalar, is written below: δW = τ T21 ⋅ δ Ω1 − τ T21 ⋅ δ Ω 2 − τ T32 ⋅ δ Ω 2 + τ T32 ⋅ δ Ω 3

(2.18)

The above expression is written in such away that a positive torque is applied on links 1 and 3 with equal and opposite components applied to link 2. The components of the generalized force vector, Q , are found as follows:

Q=

∂δW ∂ (δ q )

(2.19)

28

Equations of Motion

The system energies are expressed as a function of the generalized coordinates and physical constants only after the application of the kinematic constraints in equations 2.710. The Lagrangian is then:

L( q ,q& ) = T − V

(2.20)

The Euler-Lagrange equations28 can now be applied to derive the equations of motion:

d  ∂L dt  ∂q& j

 ∂L − = Qj  ∂q j 

j = 1..12

(2.21a)

One can write the Lagrangian in the form:

L=

1 ∑ q&i M ij q& j − V (qi ) 2 i, j

(2.21b)

Where M ij denotes a symmetric positive definite inertia matrix that is a function of qi , but not q& i . The Euler-Lagrange equation can be written as:

∑M j

ij

∂M jk 1 ∂V q&& j + ∑ M& ij q& j − ∑ q& j q& k + = Qi 2 j ∂qi ∂qi j

(2.21c)

or:

& ⋅ q& − 1 q& ∂M q& + ∂V = Q && + M M⋅q 2 ∂q ∂q&

(2.21d)

Conversion to State Space Equation 2.21a is a system of twelve second order nonlinear coupled differential equations. Finding a closed form analytical solution is out of the question which leaves

29 solution by numerical methods. The first step is to convert the above system of twelve second order equations into a system of 24 first order equations.

This is done by

assigning state variables according to the following relationships:

s i = qi s i +12 = q& i

i = 1..12

(2.22)

The system of equations can be rewritten using the above relations as:

012  s& = A ⋅ s + B ⋅    &q& 

(2.23a)

where 012×12 A= 012×12

112×12  012×12 

012×12 B= 012×12

012×12  112×12 

(2.23b)

&& is and 012×12 and 112×12 denote the 12 × 12 null and identity matrices respectively. Here q && . The complexity of the to be understood as the vector given by solving 2.10d for q equations of motion makes this very cumbersome and difficult. The key to solving these equations is that they are quasilinear, meaning that the second derivatives may have nonlinear coefficients but enter linearly. The system can be written as follows:

&& + D( q , q& , τ ) = 0 C( q , q& ) ⋅ q

(2.24)

At this point, it is most useful to consider a simple example system of the same form and completely run through the solution technique. shown in Figure 2.2.

Consider the inverted pendulum as

30

Figure 2.2: Example System which produces the following 4th order differential system of equations:

(M + m)&x& + ml cos(θ )θ&& − ml sin(θ )θ& 2 = F ml cos(θ )&x& + ml 2θ&& − ml sin (θ )x&θ& − mgl sin (θ ) = 0

eq1 : eq 2 :

(2.25)

The first step is to solve the first equation for &x& :

&x& =

F ml ml − cos(θ )θ&& + sin (θ )θ& 2 M +m M +m M +m

(2.26)

2.26 can be rewritten as follows:

C1 = −

ml cos(θ ) M +m

&x& = C1θ&& + C 2 ml F , C2 = sin (θ )θ& 2 + M +m M +m

(2.27)

The next step is to solve the second equation for θ&& . 1 g 1 θ&& = sin (θ )x&θ& + sin (θ ) − cos(θ )&x& l l l

(2.28)

Equation 2.27 can be substituted into 2.28 producing:

(

1 g 1 θ&& = sin (θ )x&θ& + sin (θ ) − cos(θ ) C1θ&& + C 2 l l l

)

(2.29)

31 Now resolve 2.29 for θ&& and assign another coefficient:

sin (θ )x&θ& + g sin (θ ) − C 2 cos(θ ) θ&& = l + C1 cos(θ ) θ&& = C

sin (θ )x&θ& + g sin (θ ) − C 2 cos(θ ) l + C1 cos(θ ) 3

C3 =

(2.30)

The final step is to back substitute into 2.27 using 2.30.

&x& = C1C 3 + C 2

(2.31)

This method can be applied on a larger scale to the system in question in order to greatly reduce the amount of numerical computations and subsequent computation time. The system is too cumbersome to solve numerically without employing the use of the coefficients. The solution for q&& produces 54 coefficient constants which can be found listed in the Appendix B. The results come out in the following form:

&& = f ( C1 ...C 54 ) q

C i = f ( C1 ...C( i −1 ) , s ,τ )

i = 1..54

(2.32)

Data Manipulation This section describes the calculations run after the integration has been completed and the entire state matrix is populated. The state matrix is then used to compute the centers of mass, momenta, and link kinematics.

System Center of Mass The results generated by the integration need to be manipulated to obtain the data for the positions and the velocities of the COMs of the first and third rod. This is done using

32 equations 2.5 and 2.7 respectively. The center of mass of the entire system can be found in terms of the individual COMs as follows:

 m1 x1 + m 2 x 2 + m3 x3    m1 + m2 + m3   xc    m1 y1 + m2 y 2 + m3 y 3        yc  =    z   m1 + m 2 + m3  c  m1 z1 + m2 z 2 + m3 z 3       m1 + m2 + m3 

(2.33)

The velocity of this point can be found by differentiating the above expression with respect to time:

 m1 x&1 + m2 x& 2 + m3 x& 3    m1 + m2 + m3    x& c   & & &     m1 y1 + m2 y 2 + m3 y 3    y& c  =   z&   m1 + m2 + m3   c  & m1 z1 + m2 z& 2 + m3 z& 3       m1 + m2 + m3 

(2.34)

The only external force is that of gravity. So one would expect the speed of the system’s COM to be − gt k if starting from rest.

Linear and Angular Momentum The linear momentum of the system is straightforward, simply the sum of the linear momenta of the individual bodies.

p = ∑ m i r&i 3

(2.35)

i =1

The angular momentum is a little more challenging and it is actually helpful to calculate this from first principles by integrating the differential angular momentum

d H = r × dm r&

(2.36)

33 over the entire system volume. In order to perform the integrations over the volume, variables of integration need to be introduced into the position and velocity vectors written in the spatial frame. Let ρ i denote the position of an arbitrary point in body i . Then

η 1 a1    ⋅ ζ 1b1  ξ c   1 1  x& 2  0 0 η 1 a1    &T   &T   &T   ρ& 1 =  y& 2  − R 2 ⋅  0  − R 1 ⋅  0  + R 1 ⋅ ζ 1b1   z&  c  c  ξ c   2  2  1  1 1 η 2 a 2   x2     T  ρ 2 =  y 2  + R 2 ⋅ ζ 2 b2  z  ξ c   2 2  2 0   ⋅  0  − R 1T c   2

0   ⋅  0  + R 1T c   1

η 2 a 2    ⋅ ζ 2 b2  ξ c   2 2  x2  0    T  ρ 3 =  y 2  + R 2 ⋅  0  + R T3 z  c   2  2  x& 2  0   &T   &T ρ& 3 =  y& 2  + R 2 ⋅  0  + R 3  z&  c   2  2

0   ⋅  0  + R T3 c   3

 x2    ρ 1 =  y 2  − R T2 z   2

 x& 2    &T ρ& 2 =  y& 2  + R 2  z&   2

η 3 a 3    ⋅ ζ 3 b3  ξ c   3 3 0 η 3 a 3    &T   ⋅  0  + R 3 ⋅ ζ 3 b3  c  ξ c   3  3 3

(2.37)

where η , ξ , ζ all range from -1 to +1. Thus dm = m i dζ i dξ i dη i ri = ρ i r&i = ρ& i

(2.38)

The angular momentum of the entire system with respect to the spatial origin can be as follows:

34

∫ ∫ ∫ [ρ1 × m1 ρ& 1 ]dη1 dζ 1 dξ 1 + ∫ ∫ ∫ [ρ 2 × m2 ρ& 2 ]dη 2 dζ 2 dξ 2 1 1 1

1 1 1

−1 −1 −1

−1 −1 −1

H= +

∫ ∫ ∫ [ρ 1 1 1

3

× m3 ρ& 3 ]dη 3 dζ 3 dξ 3

(2.39)

−1 −1 −1

The rate of change of the angular momentum with respect to the spatial origin is found by differentiating each element of the vector as follows: & = d H H dt

(2.40)

The external torque on the system about the origin should always be equal to the rate of change of the angular momentum about the origin. Equation 2.18 writes the joint torque as equal and opposite on connected links which causes them to cancel in the external torque expression. The forces acting on each of the rods in the spatial frame are:  0    fi =  0  − m g   i 

(2.41)

Using the above expression the net external torque about the origin becomes:

τ O = ∫ ∫ ∫ [ρ 1 × f1 ]dη 1 dζ 1 dξ 1 + ∫ ∫ ∫ [ρ 2 × f 2 ]dη 2 dζ 2 dξ 2 1 1 1

1 1 1

−1 −1 −1

−1 −1 −1

+

∫ ∫ ∫ [ρ 1 1 1

3

× f 3 ]dη 3 dζ 3 dξ 3

(2.42)

−1 −1 −1

The behavior of the linear and angular momenta can be used to check the simulation.

Uncontrolled Test Simulations This section presents three simulations of the system in free fall with the control torques removed. The goal is to create simulations where the system should have predictable results in order to assess the validity of the model.

35

Simulation Overview The commercial package MATLAB has numerical routines built into it which makes it straightforward to solve the system using the Runge-Kutta-Fehlberg (RKF45) recipe. It must be provided with numerical values for all of physical constants and the 24 initial states of the system. After simulation, the MATLAB function returns numerical values for each of the 24 states and the corresponding time value. The physical parameters found in table 2.1 are used for this section:

Link 1 Link 2 Link 3

m (kg) 75 75 75

a (m) .25 .25 .25

b (m) .25 .25 .25

c (m) .75 .75 .75

Jx (kg m2) 15.63 15.63 15.63

Jy (kg m2) 15.63 15.63 15.63

Jz (kg m2) 3.13 3.13 3.13

Table 2.1: Physical Parameters

Uncontrolled test simulations can easily be achieved with this model by setting of gains the in PD controls equal to zero as in table 2.2:

KZ KX KY JZ JX JY

τ 21 (Nm) 0 0 0 0 0 0

τ 32 (Nm) 0 0 0 0 0 0

Table 2.2: Gains The full simulation code and any accompanying functions can be found in Appendix B.

Case 1 – Simple Free Fall The first case to investigate is simple free fall from the “prone” position. This means the system is extended straight out along the inertial Y axis, with all links collinear and no

36 initial motion.

The system should remain in the YZ plane and fall straight down,

maintaining the orientation seen in figure 2.3:

Figure 2.3: Case 1 Expected Results This simulation is run with the initial conditions in table 2.3:

X Y Z φ θ ϕ & X & Y & Z φ&

(m) (m) (m) (rad) (rad) (rad) (m/s) (m/s) (m/s) (rad/s)

θ& (rad/s) ϕ& (rad/s)

Link 1 0 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/2 0 0

0 0

0 0

0 0

Table 2.3: Case 1 Initial Conditions The following figures display the results after a 1 second simulation:

37

Figure Set 2.4a: Case 1 Results

38

Figure Set 2.4b: Case 1 Results The previous figure set agrees well with expected results. The COM position plot shows that links 1, 2, and 3 begin at the origin. The motion is linear and 1D in a free fall along the negative Z axis. Also, this plot indicates that COM location of the system is equal to the COM of link 2 which is expected because of symmetry. The second set of plots shows that the vertical velocity is increasing linearly indicating a constant acceleration. The velocity at a time of 1 second is 9.81 m/s which correctly corresponds to 1 second of gravitational acceleration. The final plot shows no angular velocity around the body axes confirming no rotation occurs.

This case can be generalized to any set of initial conditions which include all of the time derivatives being set equal to zero. The equal acceleration acting on all 3 COMs causes

39 no change in the systems configuration. Links of different masses and sizes will affect the location of the system’s COM but should also see no configuration change.

Case 2 – Helix The second case is to get the system to rotate as a rigid body in the XY plane while accelerating along the –Z axis and tracing out a helix plot. This is accomplished by setting the three angular velocities about the body Y axes equal to 360 Deg/sec so the system should complete one full revolution during a 1 second simulation. The complete set of initial conditions is seen in table 2.4:

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 0 π/2 0 2π

Link 2 0 0 0 0 π/2 0 0 0 0 2π

Link 3 0 π/2 0 2π

0 0

0 0

0 0

Table 2.4: Case 2 Initial Conditions

40 A diagram of the initial system configuration can be seen in figure 2.5:

Figure 2.5: Case 2 Initial Configuration The numerical results for 1 second of simulation:


41

Figure Set 2.6b: Case 2 Results

42

The above results are in agreement with the expected motion. First, the position plot shows that the system completes one full rotation during free fall tracing out a helix with both link 2 and the system’s COMs remaining on the Z axis. The second set shows that the X and Y velocities for link 1 are a ¼ of a cycle out of phase with each other. Also, the X and Y velocities of link 1 are 180 degrees out of phase with the corresponding velocity on link 3. The final figure shows that angular velocity remains constant demonstrating no relative velocity between the links.

Case 3 – Irregular Initial Conditions & Conservation of Momentum The initial conditions for this case are set to irregular nonzero values which lead to unpredictable motion. These values were chosen after running a series of simulations with computer generated initial conditions and are representative of the type of behavior seen. As always, the starting position of the COM of link 2 can be reset to the origin without loss of generality.

There are three purposes to this case. First, the COM of the entire system should still follow a smooth parabolic path. Second, the linear momentum of the system should remain constant and non-zero along the X and Y directions while increasing linearly due to gravity along the Z direction. Third, the rate of change of the angular momentum with respect to the spatial origin should be equal to the net torque on the system about the origin. The initial conditions used are listed in table 2.5:

43

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 2.27 2.20 1.76 4.46

Link 2 0 0 0 0.76 3.37 3.49 0.60 2.25 3.57 4.32

Link 3 3.63 2.39 2.77 4.54

1.36 1.27

1.16 4.02

1.15 1.19

Table 2.5: Case 3 Initial Conditions Now the results of a 2 second simulation:


44


45

Figure Set 2.7c: Case 3 Results

46

The results confirm the expectations. The first plot shows that while the individual COMs trace random patterns, the system’s COM traces out a perfect parabola. This is reinforced by the velocity plots.

Secondly, the linear momentum of the system is

constant along the X and Y spatial axes as expected. Linear momentum along the Z axes increases linearly due to gravitational acceleration.

The last plot shows that the

difference between the rate of change of the angular momentum with respect to the origin and the net external torque about the origin stems from round-off error and is essentially zero.

47

3. Control This section discusses the strategies used in developing the control torque for this model and presents three simple test cases.

Desired States The first step in designing the controls in equation 2.16 was to determine the body configurations used by Olympic divers and gymnasts in performing their acrobatic maneuvers. In competitive diving, divers may specify one of the four following body positions during a dive29: 1. Straight – body has zero bend in both the hips and the knees 2. Pike – body is bent over at the hips, but the knees remain straight 3. Tuck – legs are bent at knees with the knees brought up to the chest 4. Free – any combination of the above three The goal of the controls is to use the three link system in this document to recreate the following analogous configurations shown in figure 3.1:

Figure 3.1: Analogous Configurations

48

Gain Selection Equation 2.16 introduces six proportional and six velocity gains which must be chosen to ensure both stable convergence to the desired state and adequate response parameters. Physically it is desirable to minimize convergence time, the number of oscillations, and overshoot before convergence. In the linear control world there are theories, such as pole placement, used to determine the gains. The changes from initial to final configuration are too large for a linear approximation. In addition the error functions are inherently nonlinear. This leaves empirical methods for gain selection, which essentially amount to trial and error.

After many trials a few trends were discovered to aid in gain selection. First, the general magnitude of the torque is determined by the magnitude of the gains. The larger the individual links, the larger the gains have to be for adequate response time. The physical dimensions play a larger role in the size of the gains than the mass of the links themselves. Secondly, it was empirically determined through trial and error that velocity gains of

1 2

of the proportional gains produce a damped response with minimal

oscillation. If the values are too low too many oscillations occur before the response damps out. Results show that this ratio corresponds pretty closely to critical damping. Next, the cross product between the z axes of two bodies is zero both when the included angle is 180 degrees and when it is zero degrees (straight vs. tuck) because the vectors are parallel in both cases. The position to which the control drives the system into depends on the sign of the gains. If the z axes gains are negative and the rods are collapsing on each other, switching the signs of both gains (proportional and derivative)

49 will cause them to extend. Finally, the control built using the x or y axis cross product can be treated as a secondary control and only requires gains that are 1/5th of the z axis control.

Only one of the secondary controls is needed in any given situation which

means the other one is set to zero. Failure to do so results in instability. Which one is used depends on axis of the desired rotation. For straightening movements, they are interchangeable.

Physical Interpretation Equations 2.16 list the control torques in the spatial frame. If everything remains in plane this makes perfect physical sense as spatial axis which the torque is about remains parallel to its corresponding body axis. However, when motion begins to leave the plane the feasibility of physically implementing torques about the inertial axes disappears. One way to construct physically realizable torques is to rotate the torque vector written in the spatial frame to the body axes of the link at which the torques are generated. Consider the following concept.

50

Figure 3.2: Motor Driven Ball Joint Concept Figure 3.2 shows the female part of the joint fitted with driven friction rollers which are capable of transferring torque between the ball and cup. There are two rollers for the x and y body axes and four for the z axis. The torque for each roller (body axes) can be computed from the spatial torque vector as follows: τ 1 = R1 ⋅ τ 21 τ 3 = R3 ⋅ τ 32

As written, equation 3.1 indicates links 1 and 3 would apply the torques. link would be a recipient of their equal and opposite components.

(3.1)

The middle

51

Another concept which may be feasible involves linear electric motors. Magnets would be imbedded in the ball and an alternating current run through the cup. This concept is most feasible for rotation about a single axis. The idea still remains though of being able to provide torque generation in one link and equal and opposite reactions on the other thus conserving angular momentum.

Controlled Test Cases – Overview Three simple test cases demonstrate the abilities of the model. The first is the realignment of the links from a nonplanar configuration into a straight collinear position. The second case demonstrates the models ability to resist the initial rotation of individual links and maintain a straight position. The final case demonstrates the models ability to drive the cross product to non-zero constants. For these simulations, the links are chosen to be of equal length and mass. The acceleration of gravity, g , is 9.81 m/s2. The remaining physical constants are shown in table 3.1:


m (kg) 75 75 75

a (m) .25 .25 .25

b (m) .25 .25 .25

c (m) .75 .75 .75

Jx (kg m2) 15.63 15.63 15.63

Table 3.1: Physical Parameters

Jy (kg m2) 15.63 15.63 15.63

Jz (kg m2) 3.13 3.13 3.13

52 The control gains were chosen as follows:

KZ KX KY JZ JX JY

τ 21 (Nm) 500 100 0 353.55 70.71 0

τ 32 (Nm) -500 -100 0 -353.55 -70.71 0

Table 3.2: Gains

Case 1 – Straightening of a 3D Initial Configuration The goal of this simulation is to take a model whose initial configuration is not contained in a 2D plane and use the control torques to extend the links into the straight position. The initial conditions are listed in table 3.3:

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 π/2 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/1800 0 0

0 0

0 0

0 0


θ 3 is chosen to be

π 1800

rad because zero constitutes a singularity caused by a

numerical division by zero preventing integration.

Any configuration angle can be

53 chosen and still achieve the same affect, but this choice makes it easier to draw and visualize. The physical representation of the above initial conditions is shown in figure 3.3:

Figure 3.3: Case 1 Initial Configuration

Below are results for a 3 second simulation:

54


55


56


57 Figure set 3.4 demonstrates that the model behaves in the desired manner. The COM plot and the Euler angle plots both show that the system straightens out with each Euler angle approaching the same value across all 3 links. This means the control torques were able to accomplish the desired path.

The angular velocity plot shows that there is zero

angular velocity in the system after it straightens out indicating steady state has been reached. This is to be expected because the system must conserve angular momentum and the initial angular momentum was zero. This plot also shows that system response time is about 2.5 seconds before all motion is damped out. The plot of the control torques shows that the majority of the control effort is completed after approximately 1 second and that the magnitudes of the torques are on par with the proportional gains selected for this simulation. The cross product plot shows that the desired state of a zero cross product was achieved. Finally, the last plot set shows that the angular momentum is correctly conserved for the system.

Case 2 – Resistance of Initial Angular Velocities in 2 Links The goal of this simulation is to investigate the control’s ability to hold the system in the straight position when one or more of the links have an initial angular velocity. Links 1 and 3 will be given equal and opposite angular velocities about their x body axes.

If

everything stays in plane and the control torque is identical the movements should offset each other and the system should not rotate when it reaches steady state. The initial conditions are listed in table 3.4:

58

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 0 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/2 0 0

4π 0

0 0

-4π 0


A physical representation of this is seen in figure 3.5:

Figure 3.5: Case 2 Initial Configuration

The results of a 3 second simulation are:

59


60


61


62

The results of this simulation agree with the expected results. The first two figures show that the links straighten out and translate along the z axis for a period of time.

This

phenomenon occurs as a result of the links having unequal initial angular velocities and can be thought of as a “whipping” affect. The Euler angle plot shows the angles for links 1 and 3 initially deviate from their start value but return to their original value exactly. The Euler angles for link 2 don’t change, suggesting the torque at both joints is equal and opposite. The body angular velocity plot confirms there is zero rotation once the desired state is reached. The next plot confirms the previous conclusion that the torque at both joints balances itself. The torque is much higher for this case than case 1 due to having to resist both inertia with angular momentum where as the previous case just had to resist inertia.

The last plot shows that the cross product actually deviates almost 60 degrees

from the desired state of zero before the control can “catch” it.

63

Case 3 – 2D Non-collinear Desired State The third test case demonstrates the control’s ability to drive the desired cross product to a nonzero value.

This test will also demonstrate that an athlete can rotate mid-flight

even without possessing any angular momentum. The goal for this test is to drive link 1 through a 30 degree angle change and link 3 through a 60 degree angle change. The unbalanced movement should cause the middle link to rotate in order to offset the extra 30 degrees of rotation by link 3. The initial conditions for this case are in table 3.5:

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 0 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/2 0 0

0 0

0 0

0 0


64 The desired cross product between the z body axes are listed in equation 3.2:

rd z 21

rd z 32

1 d 11      2 = d 12  =  0  d   0   13       d 31      = d 32  =  d    33   

3  2  0  0   

(3.2)

The configuration of the desired state is shown below without accounting for the rotation of link 2:

Figure 3.7: Case 3 Desired State

Results from a 3 second simulation:

65


66


67


68 This case agrees well with the expected results. The Euler angle plot shows that as the rotation away from the starting position occurs the middle link also begins to rotate. Numerical values show this change is roughly 10 degrees.

The body angular velocity

plot shows that the rotation rate has dropped to zero by the end of the simulation. Also of note, link 1 and link 3 rotate in opposite directions in order to conserve momentum. The plot of the cross products between the body axes show that system is able to achieve the desired state and in doing so the joint angle changes are 30 and 60 degrees as desired. The last plot shows that despite the system’s rotation the angular momentum correctly remains conserved.

69

4. Simulations Chapter 3 demonstrates that the control strategy based on applying a standard PD control to vector errors defined by cross products works in principle to both two and three dimensional cases.

This section presents two complex simulations designed to

demonstrate the model’s ability to mimic several common diving maneuvers. The goal of case 1 is to investigate the model’s ability to reproduce the inertia changes associated with three common (2D) diving positions using the analogous configurations mentioned in chapter 3. The goal of case 2 is to investigate the 3D motion a diver would use to generate a twist by beginning with the system rotating in a 2D plane and then attempting to induce out of plane motion rotation. This can be visualized with the help of Figures 4.1a and 4.1b. The first shows the system rotating in the YZ plane with all rotation about the X spatial axis:

70

Figure 4.1a: System Pre-Twist Maneuver After the twist maneuver has been completed, the system still rotates about the X spatial axis despite it and the x body axis no longer being parallel. This is seen in Figure 4.1b:

71

Figure 4.1b: System Post-Twist Maneuver

The mid-flight configuration changes described in this section are accomplished using a modified version of the main routine (Main.m) listed in Appendix B. This new routine uses two or three numerical integrations sequentially. Each successive simulation gets a new goal (Constants.m) and uses the final state of the previous segment for initial conditions. The individual result arrays can then be combined together into a single state matrix and time vector to take advantage of data manipulation routines. functions (Main.m) for the cases in this chapter can be found in Appendix C.

The main

72 The following two cases simulate 20 seconds of freefall. During this the time systems falls approximately 2 km. This is unrealistic for a model of competitive diving and even skydiving because air resistance is neglected allowing the system to continue its gravitational acceleration.

A sky diver reaches terminal velocity and freefalls at

approximately 110 mph or 50 m/s30. This velocity is surpassed long before 20 seconds according to the results. This time length was chosen because the control gains produce a maximum net joint angular velocity (difference between the angular velocities of adjoining links) of approximately 800 Deg/sec which corresponds to empirical data on human joints31. This will be discussed in detail in chapter 5.

Case 1 – System Configuration & Rotational Inertia This case involves 3 separate configurations strung together into one free-fall. The 3 system configurations used are analogous to the straight, pike, and tuck body positions used in competitive diving. Link 1 is considered analogous to both legs below the knee joint. Link 2 is considered analogous to both thighs. Link 3 becomes analogous to the torso including the arms and head. The masses and dimensions of each link relative to the other links are chosen to approximately represent a 6 ft tall and 170 lb diver. The average density of 1070 kg/m3 provided by Yeadon32 was used. The physical dimensions of all three links are set to be equal in order to aid the geometric interpretation of the results and make it easy to solve for them using the density, mass, and height of the diver. The mass of the individual links are staggered to approximate the differences in rotational inertia seen in real life. The acceleration of gravity, g , is 9.81 m/s2. The remaining physical parameters are found in table 4.1:

73


m (kg) 20 25 30

a (m) .1 .1 .1

b (m) .1 .1 .1

c (m) .3 .3 .3

Jx (kg m2) .67 .83 1

Jy (kg m2) .67 .83 1

Jz (kg m2) .13 .17 .20

Table 4.1: Case 1 Physical Parameters The 20 second simulation is divided into three sections. In the first section (0 < t < 5) , the system is extended in the collinear straight position. Link 3 is given an initial angular velocity and the controls are asked to hold the configuration so the system rotates as a rigid body. In the second section (5 < t < 10) , the sign of KZ 32 is changed causing links 2 and 3 to collapse, assuming the pike position. The third section (10 < t < 20) changes the sign of KZ 21 which collapses link 1 on links 2 and 3 resulting in the tuck position. Figure 4.2 shows a schematic:

Figure 4.2: Case 1 Desired States

74 The following initial conditions seen in table 4.2 are used at t = 0 : X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 0 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/2 0 0

0 0

0 0

π/3 0

Table 4.2: Case 1 Initial Conditions The control gains for 0 < t < 5 are chosen to have the correct signs for the model to remain elongated and a magnitude which was found by trial and error to provide a smooth stable response. This corresponds to section I in figure 4.2:

KZ KX KY JZ JX JY

τ 21 (Nm) 25 5 0 17.68 3.54 0

τ 32 (Nm) -25 -5 0 -17.68 -3.54 0

Table 4.3: Case 1 Segment I Gains

75 The control gains for 5 < t < 10 change only sign of KZ 32 to collapse links 2 and 3. This corresponds to section II in Figure 4.2:

KZ KX KY JZ JX JY

τ 21 (Nm) 25 5 0 17.68 3.54 0

τ 32 (Nm) 25 -5 0 17.68 -3.54 0

Table 4.4: Case 1 Segment II Gains The control gains for 10 < t < 20 change the sign of KZ 21 to collapse links 1 and 2. This corresponds to section III in Figure 4.2:

KZ KX KY JZ JX JY

τ 21 (Nm) -25 5 0 -17.68 3.54 0

τ 32 (Nm) 25 -5 0 17.68 -3.54 0

Table 4.5: Case 1 Segment III Gains The complete results for the 20 second simulation are as follows with the sections from figure 4.2 labeled when appropriate:

76


77


78


79

Figure Set 4.3d: Case 1 Results

80 Figure 4.1 can be redrawn to help easily understand the results:

Figure 4.4: Case 1 General Results A general observation from the results is that system’s configuration makes a big difference in the system’s rotation speed. The system began freefall with flexible joints and a finite amount of angular momentum stored in link 3. The control torques force the joints to become rigid causing all 3 links to move as one body. This leads to a transfer of angular momentum in link 3 to the entire body causing a rotation of 17 Deg/s in the straight position. At 5 seconds, the system changes configuration to the pike position. The system rotates at 43 Deg/s once the control torque reaches steady state compared to the initial realignment of the system configuration and the joints again become rigid. This is an increase of 252% in rate of rotation. Similarly, at 10 seconds the system changes to the tuck position producing a rigid body rotation of 136 Deg/s. This is an increase of 800% over the straight position and 316% over the tuck position.

81 The results help to explain why 20 seconds of simulation were required.

Angular

velocity data demonstrate that the maximum net joint angular velocity remains within 1 rotation per second of the previously mentioned limit. The cross product data show that the control remains active for 4 of the 5 seconds in segment II and 6 of the 10 seconds in segment III.

Case 2 – Generating Twist This case attempts to reproduce the maneuver in competitive diving used to initiate a twist. The maneuver involves generating an off axis, out of plane, rotation creating misalignment between the body angular velocity vector and the inertial angular momentum vector. This leads to angular velocities about the other body axes. The ideal maneuver to perform would be a full 360 degree rotation of a single link about its body y axis while the entire system is rotating about the inertial X axis (YZ plane).

The control is not capable of achieving the ideal motion, but an investigation into the behavior of this motion can begin with a case that does initially reach steady state before migrating away. This simulation is divided into two stages. The first stage is similar to the first stage of case 1 where link 3 is given an initial angular velocity in the YZ plane and the control torque is set to make the system rotate as a rigid body. Once the system is rotating as a rigid body, an out of plane rotation is given to link 3 about its body y axis with the goal of reaching a fixed cross product.

82 The physical parameters remain unchanged from case 1 and can be found in table 4.1. The initial conditions for this simulation are:

X Y Z φ θ ϕ & X & Y & Z φ&



Link 1 0 π/2 0 0

Link 2 0 0 0 0 π/2 0 0 0 0 0

Link 3 0 π/2 0 0

0 0

0 0

π/12 0

Table 4.6: Case 2 Initial Conditions The following gains were used for the entire simulation.

KY is used instead of KX

because geometrically KX would impede the main control, KZ:

KZ KX KY JZ JX JY

τ 21 (Nm) 25 0 5 -17.68 0 3.54

τ 32 (Nm) -25 0 -5 17.68 0 -3.54

Table 4.7: Case 2 Gains

83 The desired state vector from 0 < t < 5

rd z 21

rd z 32

d 11  0     = d 12  = 0 d  0  13   

d 31  0     = d 32  = 0  d  0   33   

(4.1)

and from 5 < t < 20 :

rd z 21

rd z 32

d 11  0     = d 12  = 0 d  0  13   

d 31   0      = d 32  =  0  d  .15  33   

(4.2)

The above numbers were chosen by trial error and represent a system just below the threshold of control instability. A general representation of the above simulation is:

Figure 4.5: Case 2 Desired States Now the results from a 20 second simulation are shown in Figures 4.6a-c:

84


85


86

Figure Set 4.6c: Case 2 Results The results from this simulation demonstrate the control’s inability to accurately reproduce the twist maneuver. The physics are correct, but the control is unable to hold the desired position. The system initially arrives at the desired state, but quickly begins to migrate away from it. The COM plot shows that links begin to collapse on each other instead of holding a fixed position. The root of this can be seen in the Euler angle plot which shows that the value of φ3 changes when achieving the desired state, but then remains constant while all three θ continue to increase linearly. If the control torque was working as desired all three φ would change also as the system begins to rotate off axis. The results after the 5 seconds show the body angular velocities behave the same way they do in case 1. The angular velocity is correctly transferred from link 3 to all three of

87 them while remaining about the X axis. After the out of plane motion occurs, the angular velocity about all three body axes becomes nonzero even though all of the angular momentum remains about the X axis. This occurs because body axes are not aligned with the system axes, despite the control failing to hold a rigid configuration. The plots of the actual cross products confirm that the system does migrate away from the desired state. Finally, the angular momentum plot shows that all of the angular momentum remains about the X inertial axes and is conserved as expected.

88

5. Discussion and Conclusions The goal of this section is to recap and explain the main points of this document before offering suggestions for future work.

Results Summary The first conclusion is that the custom MATLAB code written for this model not only makes the numerical computations efficient, but also makes them possible. Standard conversion to state space for MATLAB’s integration routine leads to an error message due to the complexity of the kinematics. Maple’s numerical integration scheme applied to the standard problem also led to an error message after much computation. The custom method of state space conversion employed in this document is an excellent choice for the numerical simulation of complicated Euler-Lagrange equations of motion because all of the simulations run in this document were completed using less than 2 minutes of computation time.

This is an improvement of at least a factor of 100;

previously, the simulations would not solve after several hours of computation time. The machine used is an IBM T60p laptop with a dual core 2.00 GHz processor and 4 GB of RAM. It is running MATLAB Student Version 7.1 and Maple Student Version 10 on Windows XP SP 3.

This model also demonstrates the conservation of angular momentum during free fall, which is a key characteristic of this class of systems. The torque inserted at the joints does not contribute to the net external torque on the system and is written in a way so that adjoining links are acted on by the equal and opposite components of the control torque.

89 This is confirmed using several complex calculations, the extent of which is listed in Appendix B (Momentum.m). Several of the simulation results in the preceding sections of this document present the angular momentum of the system written about the origin, its rate of change, the net external torque on the system about the origin, and the error between the rate of change and the net torque. In all of the simulations the error shown is on the order of 10-8 which can be attributed to numerical roundoff error and confirms that this system does conserve angular momentum.

The next conclusion is that a cross product driven control is able to successfully alter the configuration of the system in certain situations, but is unable to converge to the desired state in all instances. The main problem with the control is that a linear (PD) control is being coupled with the cross product between two vectors which, by definition, is a nonlinear relationship. For the most part, it works. It is excellent at straightening the links and holding them collinear. Some of the more complicated maneuvers present difficulty. For example, test case 3 in chapter 3 is not possible if an out of plane configuration is chosen. The initial angular momentum of the system also plays a large role in the ability of the control to reach steady state. A greater amount of angular momentum leads to a lower chance of achieving the desired goal and holding it at a steady state.

When working correctly, the control can often take much longer then desired to converge to the desired state. An example of this is Case 1 in Chapter 4, which presents a 20 second simulation and amounts to roughly 2 km of free fall. This is most likely a result

90 of simple linear control being applied to a complicated nonlinear desired state.

A

possible solution to this problem is presented in the next section of this chapter.

All of the cases chosen in this document with the exception of the twisting maneuver demonstrate the control’s success. The twisting maneuver exhibits two problems with the control. The first one is that the initial conditions and desired states are chosen to be quite small because the control does not stabilize if the error becomes too large. My suspicion is that the nonlinear cross product terms change more rapidly than a linear PD control can respond to. The second control pitfall which the twisting maneuver exposes is the inability to hold the desired state. The results of the maneuver clearly demonstrate that the control allows the system to slowly collapse on itself. This phenomenon is hard to explain, but it appears the control has trouble with Euler angles changing as a function of each other. This is evidenced by the unchanging φ . Possible sources for this behavior include human error during control development or limitations involved in applying a linear control to a non-linear dynamic system.

A final conclusion is that despite the aforementioned difficulties this system it’s able to model the three standard diving positions and study the dynamics associated with each position. The first case, in chapter 4, demonstrates that during plane motion a three link model with PD cross product driven joint torques is a good way to study the inertia changes associated with the different positions used in competition.

91

Future Work The model presented in this document provides an excellent starting place for future research on the dynamics of similar systems. One suggestion for a future model better suited to study a twist is to limit the degrees of freedom at the joints. The unrestricted freedom is not necessary to complete the maneuver required to initiate a twist and only complicates the model. The cross product driven control is necessary in this case because a straightforward and unique expression of the joint angle is not available due to the unrestricted rotation at the joints. The best way to study a twist would be insert a hinge joint preventing any rotation not about the desired axis. This should simplify the form of the joint control torque also.

The control in this model often produces a rapid response initially when the error is great and then slows considerably as the desired state is approached. One suggestion for an even response is implement a gain scheduled control to adjust the gains as the system approaches the desired state to produce a smoother and decreased convergence time. This control strategy is similar in theory to the one implemented by Ng, Leung, and Tam33.

All of the links in this model were connected along their local z axes. One interesting, and more complex method would be to connect the links offset from the z axis. A human example of this geometry is the centerline of the leg not being collinear to the centerline of the torso. The formulation of the kinematics in this problem easily lends itself to a

92 connection at any set of body coordinates, but as the kinematics become more complicated a refined method of coefficients may be necessary to improve its computational efficiency.

A final suggestion for future work is to select physical parameters and types of solids better suited to the human anatomy. The height of the diver was chosen to be 6 feet, but width and depth dimensions were set equal to achieve the density requirement. The links are chosen to be of identical size in order to help the reader understand the results by taking advantage of dimensional symmetry. The masses are chosen so the density would be no less than that of balsa wood in chapters 2-3 and equal to the average density of the human body in chapter 4. This was an approximate process and care can be taken to better relate the model to an actual human. Another anatomical improvement would be to limit the range of motion of the joints. The current links are free to wrap around themselves and freely pass through each other. Both of these improvements would be a major step in the direction in a more accurate modeling of the human body.

93

Appendix A – Algebraic Derivation using Maple 10 This section contains a glossary of the variables used in the attached worksheets listed in the order they appear as well as the full Maple 10 syntax used to develop the symbolic equations of motion, any accompanying calculations, and their conversion to MATLAB syntax. The variables for each worksheet are defined in tables A1-A4.

Variable Definitions This section is split into 4 sections; one for each worksheet.

Table A1. Variables for the Equations of Motion Variable p[i], q[i], w[i] T1, T2, T3, T V Q, Qt, Qtt RHS wx[i], wy[i], wz[i] R[i], RT[i] Rdot[i], RTdot[i] S0, St0 S[1], S[3] St[1], St[3] subs_to_t eq[i] subs_from_t subs_to_SS

Description

Correspond to φi , θ i ,ψ i Kinetic energy of: Link 1, Link 2, Link 3, System Potential Energy of the System Array of generalized coordinates, first derivative of Q, 2nd derivative of Q Array of generalized force place holders Body axis angular velocities Rotation matrices, transpose of rotation matrices Time derivative of R[i], RT[i] Vector location of link 2 COM, vector velocity of link 2 COM Vector location of Link 1, Link 3 Vector velocity of link 1, link 3 Array of substitutions for generalized coordinates to functions of time Euler – Lagrange equations of motion Array of substitutions for functions of time to generalized coordinates Array of substitutions for generalized coordinates to state space variables

94

Table A2. Variables for the Generalized Forces Variable DQ VR[i] ux, uy, uz r21z, r32z r21x, r21x r21y, r32y v21z, v32z v21x, v32x v21y, v32y T1z, T3z T1x, T3x T1y, T3y T1, T3 VW F[i] subs_to_SSi Fi[j]

Description Array of virtual displacements Virtual body rotation written in the spatial frame Unit vector along the body x, y, z axis Cross product between the body z axis of links 1 and 2 and links 2 and 3 Cross product between the body x axis of links 1 and 2 and links 2 and 3 Cross product between the body y axis of links 1 and 2 and links 2 and 3 Time rate of change of r21z, r32z Time rate of change of r21x, r32x Time rate of change of r21y, r32y PD control torque for links 1 and 2 and links 2 and 3 written with the z axis cross product PD control torque for links 1 and 2 and links 2 and 3 written with the x axis cross product PD control torque for links 1 and 2 and links 2 and 3 written with the y axis cross product Combination of above 3 PD controls Virtual Work of T1, T3 Generalized force components Array of substitutions for generalized coordinates to state space variables in for loop form F[i] written with state space variables in for loop form

Table A3. Variables for the Coefficient Constants Variable Equations.txt sol[i] temp[i] teq[i] SYS C1 – C54

Description Script file containing the code used to derive the equations of motion Result of eq[i] or teq[i] solved for Qtt[i] sol[i] rewritten with C’s taking the place of actual terms eq[i] with previously solved for Qtt[i]’s substituted in Vector of Qtt’s written explicity in terms of C Constants which represent the coefficients of Qtt

95

Table A4. Variables for the Data Manipulations Variable omega[j] r0, v0 In1, In2, In3 r[i] v[i] P Ho Hodot f1, f2, f3 T

Description Vector form of (wx[i],wy[i],wz[i]) Position and velocity vectors of link 2’s COM Body coordinates of any point in the body….Contains dummy variables of integration Position vector containing variables of integration Time rate of change of r[i] Linear momentum vector Angular momentum vector written about the origin Time rate of change of Ho Force vector on the COM of links 1, 2, and 3 Net external torque vector on the system about the origin

Maple 10 Worksheets The complete maple worksheets (.mws) are present below with output removed. Grey text indicates Maple input syntax. The titles correspond to the glossary section, and the variables defined in tables A1-A4.

Equations of Motion This Maple 10 worksheet develops the Euler-Lagrange equations of motion. The generalized forces are inserted as place holder variables making them easy to change. restart; with(LinearAlgebra): with(DEtools): with(plots): with(MmaTranslator[Mma]):

Link energies T1:=1/2*m1*(xt[1]^2+yt[1]^2+zt[1]^2)+1/2*Jx1*wx[1]^2+1/2*Jy1*wy[1]^2+1/ 2*Jz1*wz[1]^2: T2:=1/2*m2*(xt[2]^2+yt[2]^2+zt[2]^2)+1/2*Jx2*wx[2]^2+1/2*Jy2*wy[2]^2+1/ 2*Jz2*wz[2]^2: T3:=1/2*m3*(xt[3]^2+yt[3]^2+zt[3]^2)+1/2*Jx3*wx[3]^2+1/2*Jy3*wy[3]^2+1/ 2*Jz3*wz[3]^2: T:=T1+T2+T3: V:=m1*g*z[1]+m2*g*z[2]+m3*g*z[3]: L:=T-V:

Generalized Coordinates and RHS place holders Q:=Array([X,Y,Z,p[1],q[1],w[1],p[2],q[2],w[2],p[3],q[3],w[3]]):

96 Qt:=Array([Xt,Yt,Zt,pt[1],qt[1],wt[1],pt[2],qt[2],wt[2],pt[3],qt[3],wt[ 3]]): Qtt:=Array([Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1],ptt[2],qtt[2],wtt[2],ptt[3 ],qtt[3],wtt[3]]): RHS:=Array([F1,F2,F3,F4,F5,F6,F7,F8,F9,F10,F11,F12]):

Body Axes Angular Velocities as functions of Euler angles for i from 1 to 3 do wx[i]:=pt[i]*sin(q[i])*sin(w[i])+qt[i]*cos(w[i]); wy[i]:=pt[i]*sin(q[i])*cos(w[i])-qt[i]*sin(w[i]); wz[i]:=pt[i]*cos(q[i])+wt[i]; end do:

Rotation Matrices for i from 1 to 3 do R1[i]:=Matrix([[cos(p[i]),sin(p[i]),0],[sin(p[i]),cos(p[i]),0],[0,0,1]]); R2[i]:=Matrix([[1,0,0],[0,cos(q[i]),sin(q[i])],[0,sin(q[i]),cos(q[i])]]); R3[i]:=Matrix([[cos(w[i]),sin(w[i]),0],[sin(w[i]),cos(w[i]),0],[0,0,1]]); R[i]:=R3[i].R2[i].R1[i]; RT[i]:=Transpose(R[i]); Rdot[i]:=Matrix(3): for j from 1 to 3 do for k from 1 to 3 do for m from 1 to 12 do Rdot[i][k,j]:=Rdot[i][k,j]+diff(R[i][k,j],Q[m])*Qt[m]: end do: end do: end do: end do: for i from 1 to 3 do R[i]:=R[i]; RT[i]:=RT[i]; Rdot[i]:=Rdot[i]; RTdot[i]:=Transpose(Rdot[i]); end do:

Kinematics The transpose of the rotation matrix is used in order to go from body coordinates to spatial coordinates. S0:=Vector([X,Y,Z]): St0:=Vector([Xt,Yt,Zt]):

Link 1 S[1]:=S0-RT[2].Vector([0,0,l2/2])-RT[1].Vector([0,0,l1/2]): St[1]:=St0-RTdot[2].Vector([0,0,l2/2])-RTdot[1].Vector([0,0,l1/2]):

97 Link 2 (formality) S[2]:=S0: St[2]:=St0:

Link 3_ S[3]:=S0+RT[2].Vector([0,0,l2/2])+RT[3].Vector([0,0,l3/2]): St[3]:=St0+RTdot[2].Vector([0,0,l2/2])+RTdot[3].Vector([0,0,l3/2]):

Assign the Individual Components to their respective variables for i from 1 to 3 do x[i]:=S[i][1]; y[i]:=S[i][2]; z[i]:=S[i][3]; xt[i]:=St[i][1]; yt[i]:=St[i][2]; zt[i]:=St[i][3]; end do:

Check Lagrangian ... (all variables should be in terms of generalized coordinates) L:=L:

Substitution set to make the variables functions of time subs_to_t:=X=X(t),Y=Y(t),Z=Z(t),Xt=diff(X(t),t),Yt=diff(Y(t),t),Zt=diff (Z(t),t): for i from 1 to 3 do subs_to_t:=subs_to_t,p[i]=p[i](t),q[i]=q[i](t),w[i]=w[i](t),pt[i]=diff( p[i](t),t),qt[i]=diff(q[i](t),t),wt[i]=diff(w[i](t),t); end do: subs_to_t:=subs_to_t:

Form the Equations of motion for i from 1 to 12 do lq[i]:=diff(L,Q[i]); lq[i]:=subs({subs_to_t},lq[i]): lqt[i]:=diff(L,Qt[i]); lqt[i]:=subs({subs_to_t},lqt[i]): end do:

for i from 1 to 12 do eq[i]:=diff(lqt[i],t)-lq[i]=RHS[i]; end do:

Convert to State space subs_from_t := X(t) = X, Y(t) = Y, Z(t) = Z, p[1](t) = p[1], q[1](t) = q[1], w[1](t) = w[1], p[2](t) = p[2], q[2](t) = q[2], w[2](t) = w[2], p[3](t) = p[3], q[3](t) = q[3], w[3](t) = w[3], diff(X(t),t) = Xt, diff(Y(t),t) =Yt, diff(Z(t),t) = Zt, diff(p[1](t),t) = pt[1], diff(q[1](t),t) = qt[1], diff(w[1](t),t) = wt[1], diff(p[2](t),t) =

98 pt[2], diff(q[2](t),t) = qt[2], diff(w[2](t),t) = wt[2], diff(p[3](t),t) = pt[3], diff(q[3](t),t) = qt[3], diff(w[3](t),t) = wt[3], diff(X(t),`$`(t,2)) = Xtt, diff(Y(t),`$`(t,2)) = Ytt, diff(Z(t),`$`(t,2)) = Ztt, diff(p[1](t),`$`(t,2)) = ptt[1], diff(q[1](t),`$`(t,2)) = qtt[1], diff(w[1](t),`$`(t,2)) = wtt[1], diff(p[2](t),`$`(t,2)) = ptt[2], diff(q[2](t),`$`(t,2)) = qtt[2], diff(w[2](t),`$`(t,2)) = wtt[2], diff(p[3](t),`$`(t,2)) = ptt[3], diff(q[3](t),`$`(t,2)) = qtt[3], diff(w[3](t),`$`(t,2)) = wtt[3]: subs_to_SS := X = s[1],Y = s[2], Z = s[3], p[1] = s[4], q[1] = s[5], w[1] = s[6], p[2] = s[7], q[2] = s[8], w[2] = s[9], p[3] = s[10], q[3] = s[11], w[3] = s[12], Xt = s[13], Yt = s[14], Zt = s[15], pt[1] = s[16], qt[1] = s[17], wt[1] = s[18], pt[2] = s[19], qt[2] = s[20], wt[2] = s[21], pt[3] = s[22], qt[3] = s[23], wt[3] = s[24]: for i from 1 to 12 do eq[i]:=subs({subs_from_t},eq[i]); eq[i]:=subs({subs_to_SS},eq[i]); end do:

The equations of motion are ready for coefficient determination and conversion to MATLAB syntax

Generalized Forces This Maple 10 worksheet develops the PD control torque for each of the joints in the model and determines the generalized forces. It is designed to be inserted for the general place holders F1-F12 in the model. restart; with(LinearAlgebra):

with(CodeGeneration):

Coordinates Arrays Q:=Array([X,Y,Z,p[1],q[1],w[1],p[2],q[2],w[2],p[3],q[3],w[3]]): Qt:=Array([Xt,Yt,Zt,pt[1],qt[1],wt[1],pt[2],qt[2],wt[2],pt[3],qt[3],wt[ 3]]): Qtt:=Array([Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1],ptt[2],qtt[2],wtt[2],ptt[3 ],qtt[3],wtt[3]]): DQ:=Array([dX,dY,dZ,dp[1],dq[1],dw[1],dp[2],dq[2],dw[2],dp[3],dq[3],dw[ 3]]):

Rotations Matrices for i from 1 to 3 do R1[i]:=Matrix([[cos(p[i]),sin(p[i]),0],[sin(p[i]),cos(p[i]),0],[0,0,1]]); R2[i]:=Matrix([[1,0,0],[0,cos(q[i]),sin(q[i])],[0,sin(q[i]),cos(q[i])]]); R3[i]:=Matrix([[cos(w[i]),sin(w[i]),0],[sin(w[i]),cos(w[i]),0],[0,0,1]]); R[i]:=R3[i].R2[i].R1[i]; RT[i]:=Transpose(R[i]);

99

Rdot[i]:=Matrix(3): for j from 1 to 3 do for k from 1 to 3 do for m from 1 to 12 do Rdot[i][k,j]:=Rdot[i][k,j]+diff(R[i][k,j],Q[m])*Qt[m]: end do: end do: end do: end do: for i from 1 to 3 do R[i]:=R[i]; RT[i]:=RT[i]; Rdot[i]:=Rdot[i]; RTdot[i]:=Transpose(Rdot[i]); end do:

Virtual Body Rotation - in the spatial frame for i from 1 to 3 do VR[i]:=Vector([0,0,dp[i]]) + Transpose(R1[i]).Vector([dq[i],0,0]) + RT[i].Vector([0,0,dw[i]]); end do:

Directions of the body axes written in spatial coordinates and the cross product between them ux:=Vector([1,0,0]): uy:=Vector([0,1,0]): uz:=Vector([0,0,1]):

r21z:=(RT[1].uz) &x (RT[2].uz): r32z:=(RT[2].uz) &x (RT[3].uz): r21x:=(RT[1].ux) &x (RT[2].ux): r32x:=(RT[2].ux) &x (RT[3].ux): r21y:=(RT[1].uy) &x (RT[2].uy): r32y:=(RT[2].uy) &x (RT[3].uy):

Time rate of change of the above cross products v21z:=Vector(3): v32z:=Vector(3): v21x:=Vector(3): v32x:=Vector(3): v21y:=Vector(3): v32y:=Vector(3): for i from 1 to 3 do for j from 1 to 12 do v21z[i]:=v21z[i]+diff(r21z[i],Q[j])*Qt[j]; v32z[i]:=v32z[i]+diff(r32z[i],Q[j])*Qt[j]; v21x[i]:=v21x[i]+diff(r21x[i],Q[j])*Qt[j];

100 v32x[i]:=v32x[i]+diff(r32x[i],Q[j])*Qt[j]; v21y[i]:=v21y[i]+diff(r21y[i],Q[j])*Qt[j]; v32y[i]:=v32y[i]+diff(r32y[i],Q[j])*Qt[j]; end do; end do; v21z:=simplify(v21z): v32z:=simplify(v32z): v21x:=simplify(v21x): v32x:=simplify(v32x): v21y:=simplify(v21y): v32y:=simplify(v32y):

The torques are written in the spatial frame T1z, T3z are given a desired state vector T1z:=KZ1*(r21z-Vector([d11,d12,d13]))+JZ1*v21z: T3z:=KZ3*(r32z-Vector([d31,d32,d33]))+JZ3*v32z: T1x:=KX1*(r21x)+JX1*v21x: T3x:=KX3*(r32x)+JX3*v32x: T1y:=KY1*(r21y)+JY1*v21y: T3y:=KY3*(r32y)+JY3*v32y:

Combine the Torques T1:=T1z+T1x+T1y: T3:=T3z+T3x+T3y:

Virtual Work VW:=collect(simplify(Transpose(T1).VR[1]-Transpose(T1).VR[2]Transpose(T3).VR[2]+Transpose(T3).VR[3]),[dX,dY,dZ,dp[1],dq[1],dw[1],dp [2],dq[2],dw[2],dp[3],dq[3],dw[3]]):

Generalized Forces for i from 1 to 12 do F[i]:=simplify(diff(VW,DQ[i])); end do:

Substitutions to SS and 'for loop' form unassign('i'); subs_to_SSi := X = s[i,1],Y = s[i,2], Z = s[i,3], p[1] = s[i,4], q[1] = s[i,5], w[1] = s[i,6], p[2] = s[i,7], q[2] = s[i,8], w[2] = s[i,9], p[3] = s[i,10], q[3] = s[i,11], w[3] = s[i,12], Xt = s[i,13], Yt = s[i,14], Zt = s[i,15], pt[1] = s[i,16], qt[1] = s[i,17], wt[1] = s[i,18], pt[2] = s[i,19], qt[2] = s[i,20], wt[2] = s[i,21], pt[3] = s[i,22], qt[3] = s[i,23], wt[3] = s[i,24]: for j from 1 to 12 do Fi[j]:=subs({subs_to_SSi},F[j]); end do:

101

subs_to_SS := X = s[1],Y = s[2], Z = s[3], p[1] = s[4], q[1] = s[5], w[1] = s[6], p[2] = s[7], q[2] = s[8], w[2] = s[9], p[3] = s[10], q[3] = s[11], w[3] = s[12], Xt = s[13], Yt = s[14], Zt = s[15], pt[1] = s[16], qt[1] = s[17], wt[1] = s[18], pt[2] = s[19], qt[2] = s[20], wt[2] = s[21], pt[3] = s[22], qt[3] = s[23], wt[3] = s[24]: for j from 1 to 12 do F[j]:=subs({subs_to_SS},F[j]); end do:

Matlab for Gen. Forces for j from 1 to 12 do Matlab(F[j],output="Ts.m"); end do;

Torque Magnitudes or Control Effort Code Generation unassign('i'); subs_to_SSi := X = s[i,1],Y = s[i,2], Z = s[i,3], p[1] = s[i,4], q[1] = s[i,5], w[1] = s[i,6], p[2] = s[i,7], q[2] = s[i,8], w[2] = s[i,9], p[3] = s[i,10], q[3] = s[i,11], w[3] = s[i,12], Xt = s[i,13], Yt = s[i,14], Zt = s[i,15], pt[1] = s[i,16], qt[1] = s[i,17], wt[1] = s[i,18], pt[2] = s[i,19], qt[2] = s[i,20], wt[2] = s[i,21], pt[3] = s[i,22], qt[3] = s[i,23], wt[3] = s[i,24]: for j from 1 to 3 do T1[j]:=subs({subs_to_SSi},T1[j]); T3[j]:=subs({subs_to_SSi},T3[j]); end do: Matlab(T1,output="Controls.m"); Matlab(T3,output="Controls.m");

Coefficient Constants This Maple 10 worksheet reads in the Euler- Lagrange equations of motion and the coordinate arrays from the previous worksheet. The coefficients solved for in this worksheet were copied to a blank worksheet (not shown) and converted to MATLAB code restart: with(LinearAlgebra): with(DEtools): with(plots): with(MmaTranslator[Mma]): with(CodeGeneration): read "Equations.txt":

Determine the Coefficients The first 3 equations don't require any back substitution... i.e eq[2] doens't have Xtt in it

102 EQ1 for solved for Xtt sol[1]:=collect(solve(eq[1],Qtt[1]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1],p tt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[1]:=C1*ptt[1]+C2*qtt[1]+C3*ptt[2]+C4*qtt[2]+C5*ptt[3]+C6*qtt[3]+C7 : for i from 4 to 12 do coeff(sol[1],Qtt[i]): end do:

EQ2 for Ytt sol[2]:=collect(solve(eq[2],Qtt[2]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1],p tt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[2]:=C8*ptt[1]+C9*qtt[1]+C10*ptt[2]+C11*qtt[2]+C12*ptt[3]+C13*qtt[3 ]+C14: for i from 4 to 12 do coeff(sol[2],Qtt[i]): end do:

EQ3 for Ztt sol[3]:=collect(solve(eq[3],Qtt[3]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1],p tt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[3]:=C15*qtt[1]+C16*qtt[2]+C17*qtt[3]+C18: for i from 4 to 12 do coeff(sol[3],Qtt[i]): end do:

EQ4 for ptt1 ..... Start back substituting teq[4]:=eq[4]: for i from 1 to 3 do teq[4]:=subs(Qtt[i]=temp[i],teq[4]) end do: sol[4]:=collect(solve(teq[4],Qtt[4]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[4]:=C19*qtt[1]+C20*wtt[1]+C21*ptt[2]+C22*qtt[2]+C23*ptt[3]+C24*qtt [3]+C25: for i from 4 to 12 do coeff(sol[4],Qtt[i]): end do:

EQ5 for qtt1 teq[5]:=eq[5]: for i from 1 to 4 do teq[5]:=subs(Qtt[i]=temp[i],teq[5]) end do:

103

sol[5]:=collect(solve(teq[5],Qtt[5]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[5]:=C26*wtt[1]+C27*ptt[2]+C28*qtt[2]+C29*ptt[3]+C30*qtt[3]+C31: for i from 4 to 12 do coeff(sol[5],Qtt[i]): end do:

EQ6 for wtt 1 teq[6]:=eq[6]: for i from 1 to 5 do teq[6]:=subs(Qtt[i]=temp[i],teq[6]) end do: sol[6]:=collect(solve(teq[6],Qtt[6]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[6]:=C32*ptt[2]+C33*qtt[2]+C34*ptt[3]+C35*qtt[3]+C36: for i from 4 to 12 do coeff(sol[6],Qtt[i]): end do:

EQ7 for ptt2 teq[7]:=eq[7]: for i from 1 to 6 do teq[7]:=subs(Qtt[i]=temp[i],teq[7]) end do: sol[7]:=collect(solve(teq[7],Qtt[7]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[7]:=C37*qtt[2]+C38*wtt[2]+C39*ptt[3]+C40*qtt[3]+C41: for i from 4 to 12 do coeff(sol[7],Qtt[i]): end do:

EQ8 for qtt2 teq[8]:=eq[8]: for i from 1 to 7 do teq[8]:=subs(Qtt[i]=temp[i],teq[8]): end do: sol[8]:=collect(solve(teq[8],Qtt[8]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[8]:=C42*wtt[2]+C43*ptt[3]+C44*qtt[3]+C45: for i from 4 to 12 do

104 coeff(sol[8],Qtt[i]): end do:

EQ 9 for wtt2 teq[9]:=eq[9]: for i from 1 to 8 do teq[9]:=subs(Qtt[i]=temp[i],teq[9]): end do: sol[9]:=collect(solve(teq[9],Qtt[9]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[1], ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[9]:=C46*ptt[3]+C47*qtt[3]+C48: for i from 4 to 12 do coeff(sol[9],Qtt[i]): end do:

EQ 10 for ptt3 teq[10]:=eq[10]: for i from 1 to 9 do teq[10]:=subs(Qtt[i]=temp[i],teq[10]): end do: sol[10]:=collect(solve(teq[10],Qtt[10]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[ 1],ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[10]:=C49*qtt[3]+C50*wtt[3]+C51: for i from 4 to 12 do coeff(sol[10],Qtt[i]): end do:

EQ11 for qtt3 teq[11]:=eq[11]: for i from 1 to 10 do teq[11]:=subs(Qtt[i]=temp[i],teq[11]): end do: sol[11]:=collect(solve(teq[11],Qtt[11]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[ 1],ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[11]:=C52*wtt[3]+C53: for i from 4 to 12 do coeff(sol[11],Qtt[i]): end do:

EQ12 for wtt 3 explicitly teq[12]:=eq[12]: for i from 1 to 11 do

105 teq[12]:=subs(Qtt[i]=temp[i],teq[12]): end do: sol[12]:=collect(solve(teq[12],Qtt[12]),[Xtt,Ytt,Ztt,ptt[1],qtt[1],wtt[ 1],ptt[2],qtt[2],wtt[2],ptt[3],qtt[3],wtt[3]]): temp[12]:=C54:

Now backsubstitute... Qtt's are entirely a functions of C's after this wtt[3]:=temp[12]: qtt[3]:=temp[11]: ptt[3]:=temp[10]: wtt[2]:=temp[9]: qtt[2]:=temp[8]: ptt[2]:=temp[7]: wtt[1]:=temp[6]: qtt[1]:=temp[5]: ptt[1]:=temp[4]: Ztt:=temp[3]: Ytt:=temp[2]: Xtt:=temp[1]:

Set up the system SYS:=Vector([s[13],s[14],s[15],s[16],s[17],s[18],s[19],s[20],s[21],s[22 ],s[23],s[24],Qtt[1..12]]):

Generate MATLAB code for i from 1 to 24 do Matlab(SYS[i],output="SYS.m"): end do:

Data Manipulations This Maple 10 worksheet develops the additional calculations to be preformed after the equations of motion are integrated. It reads in the equations of motion and generalized coordinates from the previous worksheet. restart: with(LinearAlgebra): with(DEtools): with(plots): with(MmaTranslator[Mma]): with(CodeGeneration): read "Equations.txt":

The Rotation Matrices must be outputted to run in a MATLAB for loop Write them in SS form also. unassign('i'); subs_to_SSi := X = s[i,1],Y = s[i,2], Z = s[i,3], p[1] = s[i,4], q[1] = s[i,5], w[1] = s[i,6], p[2] = s[i,7], q[2] = s[i,8], w[2] = s[i,9], p[3] = s[i,10], q[3] = s[i,11], w[3] = s[i,12], Xt = s[i,13], Yt = s[i,14], Zt = s[i,15], pt[1] = s[i,16], qt[1] = s[i,17], wt[1] =

106 s[i,18], pt[2] = s[i,19], qt[2] = s[i,20], wt[2] = s[i,21], pt[3] = s[i,22], qt[3] = s[i,23], wt[3] = s[i,24]: for j from 1 to 3 do for m from 1 to 3 do for n from 1 to 3 do R[j][m,n]:=subs({subs_to_SSi},R[j][m,n]); Rdot[j][m,n]:=subs({subs_to_SSi},Rdot[j][m,n]); end do: end do: RT[j]:=Transpose(R[j]); RTdot[j]:=Transpose(Rdot[j]); end do:

Convert the Rotations to MATLAB syntax for j from 1 to 3 do Matlab(R[j],output="Rotations.m"); Matlab(RT[j],output="Rotations.m"); Matlab(Rdot[j],output="Rotations.m"); Matlab(RTdot[j],output="Rotations.m"); end do:

Body Angular Velocities in vector and state space form for j from 1 to 3 do omega[j]:=Vector([subs({subs_to_SSi},wx[j]),subs({subs_to_SSi},wy[j]),s ubs({subs_to_SSi},wz[j])]); end do:

Output to MATLAB for j from 1 to 3 do Matlab(omega[j],output="Omega.m"); end do;

Define the Position vectors for link 2 COM r0:=Vector([X,Y,Z]): v0:=Vector([Xt,Yt,Zt]):

Redefine the Rotation matrices in terms of generalized coordinates for i from 1 to 3 do R1[i]:=Matrix([[cos(p[i]),sin(p[i]),0],[sin(p[i]),cos(p[i]),0],[0,0,1]]); R2[i]:=Matrix([[1,0,0],[0,cos(q[i]),sin(q[i])],[0,sin(q[i]),cos(q[i])]]); R3[i]:=Matrix([[cos(w[i]),sin(w[i]),0],[sin(w[i]),cos(w[i]),0],[0,0,1]]); R[i]:=R3[i].R2[i].R1[i]; RT[i]:=Transpose(R[i]); Rdot[i]:=Matrix(3): for j from 1 to 3 do for k from 1 to 3 do for m from 1 to 12 do Rdot[i][k,j]:=Rdot[i][k,j]+diff(R[i][k,j],Q[m])*Qt[m]:

107 end do: end do: end do: end do: for i from 1 to 3 do R[i]:=R[i]; RT[i]:=RT[i]; Rdot[i]:=Rdot[i]; RTdot[i]:=Transpose(Rdot[i]); end do:

Dummy variables of integration written in body coordinates In1:=Vector([xi[1]*a1,eta[1]*b1,zeta[1]*l1/2]): In2:=Vector([xi[2]*a2,eta[2]*b2,zeta[2]*l2/2]): In3:=Vector([xi[3]*a3,eta[3]*b3,zeta[3]*l3/2]):

Position vectors for any point in the 3 links r[1]:=(r0 - RT[2].Vector([0,0,l2/2]) - RT[1].Vector([0,0,l1/2])) + RT[1].In1: r[2]:=r0 + RT[2].In2: r[3]:=(r0 + RT[2].Vector([0,0,l2/2]) + RT[3].Vector([0,0,l3/2])) + RT[3].In3:

Velocity vectors for any point in the 3 links v[1]:=(v0 - RTdot[2].Vector([0,0,l2/2]) - RTdot[1].Vector([0,0,l1/2])) + RTdot[1].In1: v[2]:=v0 + RTdot[2].In2: v[3]:=(v0 + RTdot[2].Vector([0,0,l2/2]) + RTdot[3].Vector([0,0,l3/2])) + RTdot[3].In3:

Calculate the Linear Momentum P:=Vector(3): for j from 1 to 3 do P[j]:=P[j]+int(int(int(m1*v[1][j],xi[1]=-1..1),eta[1]=-1..1),zeta[1]=1..1) + int(int(int(m2*v[2][j],xi[2]=-1..1),eta[2]=-1..1),zeta[2]=1..1) + int(int(int(m3*v[3][j],xi[3]=-1..1),eta[3]=-1..1),zeta[3]=1..1); end do: P:=simplify(P):

Convert to MATLAB syntax unassign('i'); for j from 1 to 3 do P[j]:=subs({subs_to_SSi},P[j]); end do: Matlab(P,output="Momentum.m");

Angular Momentum about the origin Ho:=Vector(3): temp1:= r[1] &x (m1*v[1]): temp2:= r[2] &x (m2*v[2]):

108 temp3:= r[3] &x (m3*v[3]): for j from 1 to 3 do Ho[j]:=Ho[j]+int(int(int(temp1[j],xi[1]=-1..1),eta[1]=-1..1),zeta[1]=1..1) + int(int(int(temp2[j],xi[2]=-1..1),eta[2]=-1..1),zeta[2]=-1..1) + int(int(int(temp3[j],xi[3]=-1..1),eta[3]=-1..1),zeta[3]=-1..1); end do: Ho:=simplify(Ho):

Convert to functions of time Take the Derivative with respect to time Convert back to SS form and SS for loop form for MATLAB subs_to_SSi:=subs_to_SSi,Xtt=A[i,1],Ytt=A[i,2],Ztt=A[i,3],ptt[1]=A[i,4] ,qtt[1]=A[i,5],wtt[1]=A[i,6],ptt[2]=A[i,7],qtt[2]=A[i,8],wtt[2]=A[i,9], ptt[3]=A[i,10],qtt[3]=A[i,11],wtt[3]=A[i,12]: Hodot:=Vector(3): for j from 1 to 3 do Hodot[j]:=diff(subs({subs_to_t},Ho[j]),t); Hodot[j]:=subs({subs_from_t},Hodot[j]); Ho[j]:=subs({subs_to_SSi},Ho[j]); Hodot[j]:=subs({subs_to_SSi},Hodot[j]); end do:

Net External Torque about the origin Force vectors (Gravity on the center of mass) The control torque is not included because theoretically they should be zero. If they are not the error between the Rate of change of Angular Momentum and the net torque will not be zero. f1:=Vector([0,0,-m1*g]): f2:=Vector([0,0,-m2*g]): f3:=Vector([0,0,-m3*g]):

Calculate the Torque T:=Vector(3): temp1:= r[1] &x (f1): temp2:= r[2] &x (f2): temp3:= r[3] &x (f3): for j from 1 to 3 do T[j]:=T[j]+int(int(int(temp1[j],xi[1]=-1..1),eta[1]=-1..1),zeta[1]=1..1) + int(int(int(temp2[j],xi[2]=-1..1),eta[2]=-1..1),zeta[2]=-1..1) + int(int(int(temp3[j],xi[3]=-1..1),eta[3]=-1..1),zeta[3]=-1..1); end do: T:=simplify(T):

109 Convert to MATLAB variables for j from 1 to 3 do T[j]:=subs({subs_to_SSi},T[j]); end do:

Convert the torques and the momentum to MATLAB syntax Matlab(Ho,output="Momentum.m"); Matlab(Hodot,output="Momentum.m"); Matlab(T,output="Momentum.m");

110

Appendix B – MATLAB Numerical Model This appendix presents the 14 MATLAB routines used for numerical integration. Many of these were automatically generated using Maple 10 before being modified. This simulation is taken from case 1 in chapter 3. Any text preceded by a % is a comment. Table B1 is a guide to this appendix.

Table B1. MATLAB Numerical Model Quick Reference Routine Main.m ICS.m Constants.m SYS.m Cs.m Ts.m Csi.m Rotations.m COM.m TT.m Omega.m Controls.m Momentum.m Plots.m

Function Main Routine Initial Conditions Physical Parameters System in State Space Form Coefficient Constants Control Torques Coefficient Constants in ‘for loop’ form Rotation Matrices COM Kinematics Generalized Coordinate Accelerations Body Axis Angular Velocities Control Effort, Cross Products, & Joint Angles Linear & Angular Momentum Calculations Plot Generation

Main Routine – Main.m %General Notes %__________________________________________________________ % p = phi

q = theta

%SS Definition % s1 = X2 % s2 = Y2 % s3 = Z2 % s4 = p1 % s5 = q1 % s6 = w1

s12 s13 s14 s15 s16 s17

= = = = = =

w =psi

X2t Y2t Z2t pt1 qt1 wt1

Page 108 110 111 112 116 167 189 244 247 248 252 253 262 281

111 % % % % % %

s7 = p2 s8 = q2 s9 = w2 s10 = p2 s11 = q2 s12 = w2

s18 s19 s20 s18 s19 s20

= = = = = =

pt2 qt2 wt2 pt2 qt2 wt2

% Initialization %___________________________________________________________ clear %Start Time START = datestr(now,13) %Set up the initial conditions IC = ICS; %Declare the time variables t0=0; %Start Time t1=3; %Finish Time % Run the integration routine %___________________________________________________________ % SYS.m contains the system in state space form % t = Column Vector of the time steps % s = 24 Column State Vector with the values of the states - Lines up with the t Vector [t,s]=ode45(@SYS,[t0,t1],IC);

%Data Manipulation %____________________________________________________________ %Function Info - The variables are local to the function %Format [Returned Vars] = FunctionName ( Passed Variables) %Position And Velocity of Rods [X,V,JOINT] = COM (s); %2nd Derivatives [A] = TT (s);

- COM.m

- TT.m

%Body Angular Velocities [w1, w2, w3] = Omega (s);

-

Omega.m

%Momentum - Momentum.m [P, L, T, Ldot] = Momentum(s,A); %Joint Angles , Cross Products, Torques - Controls.m [JA1,JA2, CR1, CR2, T1, T3] = Controls (s); %Plots - Plots.m

112 %___________________________________________________________ Plots(X,s,V,t,w1,w2,w3,P,L,Ldot,T,JA1,JA2,CR1,CR2,T1,T3)

%Finish Time FINISH = datestr(now,13)

Initial Conditions – ICS.m %This script function converts initial body angular velocities to Euler Angular velocities and creates the initial state vector %Format - IC = [X,Y,Z,p1,q1,w1,p2,q2,w2,p3,q3,w3,Xt,Yt,Zt,pt1,qt1,wt1,pt2,qt2,wt2,pt3, qt3,wt3] function IC = ICS IC = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]; %Initial Positions and Velocities x2 = 0; y2 = 0; z2 = 0; xt2 = 0; yt2 = 0; zt2 = 0; %Initial Orientation p1 = 0; q1 = 90*pi/180; w1 = 0; p2 = 0; q2 = 90*pi/180; w2 = 0; p3 = 0; q3 = 90*pi/180; w3 = 0; %Initial wx1 = 0; wx2 = 0; wx3 = 0;

Body angular wy1 = 0; wz1 wy2 = 0; wz2 wy3 = 0; wz3

velocities = 0; = 0; = 0;

%Euler Angular Velocities in terms of Body angualr velocites pt1 = (cos(w1) * wy1 + sin(w1) * wx1) / sin(q1); qt1 = -sin(w1) * wy1 + wx1 * cos(w1); wt1 = (-cos(q1) * cos(w1) * wy1 - cos(q1) * sin(w1) * wx1 + wz1 * sin(q1)) / sin(q1); pt2 = (cos(w2) * wy2 + sin(w2) * wx2) / sin(q2); qt2 = -sin(w2) * wy2 + wx2 * cos(w2); wt2 = (-cos(q2) * cos(w2) * wy2 - cos(q2) * sin(w2) * wx2 + wz2 * sin(q2)) / sin(q2); pt3 = (cos(w3) * wy3 + sin(w3) * wx3) / sin(q3); qt3 = -sin(w3) * wy3 + wx3 * cos(w3); wt3 = (-cos(q3) * cos(w3) * wy3 - cos(q3) * sin(w3) * wx3 + wz3 * sin(q3)) / sin(q3); %Put them in vector form

113 IC = [x2,y2,z2,p1,q1,w1,p2,q2,w2,p3,q3,w3,xt2,yt2,zt2,pt1,qt1,wt1,pt2,qt2,wt 2,pt3,qt3,wt3];

Physical Parameters – Constants.m %This is a script file containing all of the physical constants % Gravity (m/s^2) g = 981/100; %Masses of the cylinders (kg) m1 = 75; m2 = 75; m3 = 75; %The a1 = a2 = a3 =

X Body Axes .25; .25; .25;

(1/2 Dim)

(m)

%The b1 = b2 = b3 =

Y Body Axes .25; .25; .25;

(1/2 Dim)

(m)

%The c1 = c2 = c3 =

Z body Axes .75; .75; .75;

(1/2 Dim)

(m)

%Lengths of the rods (m) l1 = 2*c1; l2 = 2*c2; l3 = 2*c3; %Moments Jx1 = (1 Jy1 = (1 Jz1 = (1

of inertia about the body axes (kg-m^2) / 3) * m1 * (b1^2 + c1^2); / 3) * m1 * (a1^2 + c1^2); / 3) * m1 * (a1^2 + b1^2);

Jx2 = (1 / 3) * m2 * (b2^2 + c2^2); Jy2 = (1 / 3) * m2 * (a2^2 + c2^2); Jz2 = (1 / 3) * m2 * (a2^2 + b2^2); Jx3 = (1 / 3) * m3 * (b3^2 + c3^2); Jy3 = (1 / 3) * m3 * (a3^2 + c3^2); Jz3 = (1 / 3) * m3 * (a3^2 + b3^2); %Control Gains (Nm) KZ1 = 500; KZ3 = -500;

KX1 = 100;

KX3 = -100;

KY1 = 0;

KY3 = 0;

114 JZ1 = KZ1/sqrt(2); JX1 = KX1/sqrt(2); JY1 = KY1/sqrt(2);

JZ3 = KZ3/sqrt(2); JX3 = KX3/sqrt(2); JY3 = KY3/sqrt(2);

%Desired state vectors d11 = 0; d12 = 0; d13 = 0; d31 = 0; d32 = 0; d33 = 0;

System in State Space Form – SYS.m % System in State Space form % ds is the time derivative of the state vector function ds=SYS(t,s) %Read the Phyiscal Constants - Constants.m Constants; %Calculate the Torques - Ts.m Ts; %Calculate all of the Coefficients - Cs.m Cs; %Evaluate the system ds = [s(13) s(14) s(15) s(16) s(17) s(18) s(19) s(20) s(21) s(22) s(23) s(24) C1 * (C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54

115 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25) + C2 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C3 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C4 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C5 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C6 * (C52 * C54 + C53) + C7 C8 * (C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 *

116 (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25) + C9 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C10 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C11 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C12 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C13 * (C52 * C54 + C53) + C14

117 C15 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C16 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C17 * (C52 * C54 + C53) + C18 C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54

118 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25 C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31 C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36 C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41 C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45 C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48 C49 * (C52 * C54 + C53) + C50 * C54 + C51 C52 * C54 + C53 C54];

Coefficient Constants - Cs.m %The coefficent constants are listed in this script file. %This includes generalized forces

F1-F12

%EQ 1 C1 = m1 * l1 * sin(s(5)) * cos(s(4)) / (m1 + m2 + m3) / 0.2e1; C2 = m1 * l1 * cos(s(5)) * sin(s(4)) / (m1 + m2 + m3) / 0.2e1;

119 C3 = (m1 * l2 * sin(s(8)) * cos(s(7)) - m3 * l2 * sin(s(8)) * cos(s(7))) / (m1 + m2 + m3) / 0.2e1; C4 = (-m3 * l2 * cos(s(8)) * sin(s(7)) + m1 * l2 * cos(s(8)) * sin(s(7))) / (m1 + m2 + m3) / 0.2e1; C5 = -m3 * l3 * sin(s(11)) * cos(s(10)) / (m1 + m2 + m3) / 0.2e1; C6 = -m3 * l3 * cos(s(11)) * sin(s(10)) / (m1 + m2 + m3) / 0.2e1; C7 = (0.2e1 * m1 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19) - m1 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 - 0.2e1 * m3 * l3 * cos(s(11)) * s(23) * cos(s(10)) * s(22) - m1 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) - m1 * l1 * sin(s(5)) * s(17) ^ 2 * sin(s(4)) + 0.2e1 * m1 * l1 * cos(s(5)) * s(17) * cos(s(4)) * s(16) - m1 * l1 * sin(s(5)) * sin(s(4)) * s(16) ^ 2 + (2 * F1) + m3 * l3 * sin(s(11)) * sin(s(10)) * s(22) ^ 2 + m3 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) - 0.2e1 * m3 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19) + m3 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 + m3 * l3 * sin(s(11)) * s(23) ^ 2 * sin(s(10))) / (m1 + m2 + m3) / 0.2e1; %EQ 2 C8 = m1 * l1 * sin(s(5)) * sin(s(4)) / (m1 + m2 + m3) / 0.2e1; C9 = -m1 * l1 * cos(s(5)) * cos(s(4)) / (m1 + m2 + m3) / 0.2e1; C10 = (m1 * l2 * sin(s(8)) * sin(s(7)) - m3 * l2 * sin(s(8)) * sin(s(7))) / (m1 + m2 + m3) / 0.2e1; C11 = (m3 * l2 * cos(s(8)) * cos(s(7)) - m1 * l2 * cos(s(8)) * cos(s(7))) / (m1 + m2 + m3) / 0.2e1; C12 = -m3 * l3 * sin(s(11)) * sin(s(10)) / (m1 + m2 + m3) / 0.2e1; C13 = m3 * l3 * cos(s(11)) * cos(s(10)) / (m1 + m2 + m3) / 0.2e1; C14 = (0.2e1 * m1 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) + m1 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 - 0.2e1 * m3 * l3 * cos(s(11)) * s(23) * sin(s(10)) * s(22) + m1 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) + m1 * l1 * sin(s(5)) * s(17) ^ 2 * cos(s(4)) + 0.2e1 * m1 * l1 * cos(s(5)) * s(17) * sin(s(4)) * s(16) + m1 * l1 * sin(s(5)) * cos(s(4)) * s(16) ^ 2 + (2 * F2) - m3 * l3 * sin(s(11)) * cos(s(10)) * s(22) ^ 2 - m3 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) - 0.2e1 * m3 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) - m3 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 - m3 * l3 * sin(s(11)) * s(23) ^ 2 * cos(s(10))) / (m1 + m2 + m3) / 0.2e1; %EQ 3 C15 = -m1 * sin(s(5)) * l1 / (m1 + m2 + m3) / 0.2e1; C16 = -(m1 * sin(s(8)) * l2 - m3 * sin(s(8)) * l2) / (m1 + m2 + m3) / 0.2e1; C17 = m3 * sin(s(11)) * l3 / (m1 + m2 + m3) / 0.2e1; C18 = -(m1 * cos(s(8)) * s(20) ^ 2 * l2 + (2 * m2 * g) + m1 * cos(s(5)) * s(17) ^ 2 * l1 + 0.2e1 * m1 * g - m3 * cos(s(8)) * s(20) ^ 2 * l2 m3 * cos(s(11)) * s(23) ^ 2 * l3 - (2 * F3) + 0.2e1 * m3 * g) / (m1 + m2 + m3) / 0.2e1; %EQ 4 C19 = (-0.4e1 * Jy1 * cos(s(6)) * sin(s(5)) * sin(s(6)) - 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C9 + 0.4e1 * Jx1 * sin(s(6)) * sin(s(5)) * cos(s(6)) - 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C2) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2);

120 C20 = 0.4e1 * Jz1 * cos(s(5)) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); C21 = (-0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C10 + m1 * sin(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * cos(s(7)) + m1 * sin(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * sin(s(7)) - 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C3) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); C22 = (-0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C4 - m1 * sin(s(5)) * sin(s(4)) * l1 * l2 * cos(s(8)) * cos(s(7)) + m1 * sin(s(5)) * cos(s(4)) * l1 * l2 * cos(s(8)) * sin(s(7)) - 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C11) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); C23 = (-0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C12 - 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C5) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); C24 = (-0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C13 - 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C6) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); C25 = (m1 * sin(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 + m1 * sin(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) * s(17) * s(18) + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) ^ 2 * s(16) * l1 ^ 2 * cos(s(5)) * s(17) - 0.8e1 * Jy1 * cos(s(6)) * sin(s(5)) ^ 2 * s(16) * sin(s(6)) * s(18) - 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C7 + 0.4e1 * Jy1 * sin(s(6)) ^ 2 * s(18) * sin(s(5)) * s(17) - (4 * F4) - 0.4e1 * Jy1 * cos(s(6)) * cos(s(5)) * s(17) ^ 2 * sin(s(6)) + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) + 0.4e1 * Jx1 * cos(s(6)) ^ 2 * s(18) * sin(s(5)) * s(17) - 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C14 - 0.8e1 * Jz1 * cos(s(5)) * s(16) * sin(s(5)) * s(17) + 0.4e1 * Jx1 * sin(s(6)) * cos(s(5)) * s(17) ^ 2 * cos(s(6)) + 0.8e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) * s(16) * cos(s(5)) * s(17) - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) * s(17) * s(18) + 0.8e1 * Jx1 * sin(s(6)) * sin(s(5)) ^ 2 * s(16) * cos(s(6)) * s(18) + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) ^ 2 * l1 ^ 2 * cos(s(5)) * s(17) * s(16) - m1 * sin(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) - m1 * sin(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 + 0.8e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) * s(16) * cos(s(5)) * s(17) + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19) - 0.4e1 * Jz1 * sin(s(5)) * s(17) * s(18)) / (-m1 * sin(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(5)) * sin(s(4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * sin(s(5)) ^ 2 - 0.4e1 *

121 Jz1 * cos(s(5)) ^ 2 + 0.2e1 * m1 * sin(s(5)) * cos(s(4)) * l1 * C1 - m1 * sin(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2); %EQ 5 C26 = (-0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C20 - 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C20 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C20 + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C20) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 - m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); C27 = (-0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C3 + m1 * cos(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * cos(s(7)) - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C21 - 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C21 - m1 * cos(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * sin(s(7)) + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C21 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C21 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C10) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 - m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); C28 = (-0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C22 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C22 + m1 * cos(s(5)) * sin(s(4)) * l1 * l2 * cos(s(8)) * sin(s(7)) + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C22 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C4 + 0.2e1 * m1 * sin(s(5)) * l1 * C16 + m1 * cos(s(5)) * cos(s(4)) * l1 * l2 * cos(s(8)) * cos(s(7)) + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C22 + m1 * sin(s(5)) * l1 * sin(s(8)) * l2 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C11) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); C29 = (-0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C5 + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C23 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C23 - 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C23 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C23 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C12) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 - m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) *

122 sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); C30 = (-0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C6 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C24 + 0.2e1 * m1 * sin(s(5)) * l1 * C17 - 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C24 + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C24 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C24 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C13) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 - m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); C31 = (0.2e1 * m1 * g * sin(s(5)) * l1 + 0.4e1 * Jz1 * s(16) * sin(s(5)) * s(18) + 0.4e1 * Jz1 * s(16) ^ 2 * sin(s(5)) * cos(s(5)) + 0.2e1 * m1 * sin(s(5)) * l1 * C18 - (4 * F5) - m1 * cos(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) - m1 * cos(s(5)) * cos(s(4)) ^ 2 * l1 ^ 2 * sin(s(5)) * s(17) ^ 2 - m1 * cos(s(5)) * sin(s(4)) ^ 2 * l1 ^ 2 * sin(s(5)) * s(17) ^ 2 - m1 * cos(s(5)) * cos(s(4)) ^ 2 * s(16) ^ 2 * l1 ^ 2 * sin(s(5)) - m1 * cos(s(5)) * sin(s(4)) ^ 2 * l1 ^ 2 * sin(s(5)) * s(16) ^ 2 - m1 * cos(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) m1 * cos(s(5)) * sin(s(4)) * l1 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 - m1 * cos(s(5)) * cos(s(4)) * l1 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 + m1 * sin(s(5)) * l1 * cos(s(8)) * s(20) ^ 2 * l2 + m1 * sin(s(5)) * l1 ^ 2 * cos(s(5)) * s(17) ^ 2 + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C14 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C25 - 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C7 - 0.8e1 * Jx1 * cos(s(6)) * s(17) * sin(s(6)) * s(18) + 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C25 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19) + 0.4e1 * Jy1 * sin(s(6)) ^ 2 * s(16) * sin(s(5)) * s(18) + 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C25 - 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C25 - 0.4e1 * Jx1 * s(16) ^ 2 * cos(s(5)) * sin(s(6)) ^ 2 * sin(s(5)) - 0.4e1 * Jy1 * s(16) ^ 2 * cos(s(5)) * cos(s(6)) ^ 2 * sin(s(5)) - 0.4e1 * Jx1 * sin(s(6)) ^ 2 * s(18) * s(16) * sin(s(5)) + 0.4e1 * Jx1 * cos(s(6)) ^ 2 * s(16) * sin(s(5)) * s(18) + 0.8e1 * Jy1 * sin(s(6)) * s(17) * cos(s(6)) * s(18) - 0.4e1 * Jy1 * cos(s(6)) ^ 2 * s(18) * s(16) * sin(s(5))) / (0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C2 - m1 * cos(s(5)) ^ 2 * sin(s(4)) ^ 2 * l1 ^ 2 0.2e1 * m1 * sin(s(5)) * l1 * C15 - m1 * cos(s(5)) ^ 2 * cos(s(4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(5)) * sin(s(4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(6)) * sin(s(5)) * cos(s(6)) * C19 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C9 - 0.2e1 * m1 * cos(s(5)) * cos(s(4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(6)) * sin(s(5)) * sin(s(6)) * C19 - m1 * sin(s(5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(6)) ^ 2 - 0.4e1 * Jx1 * cos(s(6)) ^ 2); %EQ6 C32 = -(Jz1 * cos(s(5)) * C19 * C27 + Jz1 * cos(s(5)) * C21) / Jz1 / (cos(s(5)) * C19 * C26 + cos(s(5)) * C20 + 0.1e1); C33 = -(Jz1 * cos(s(5)) * C22 + Jz1 * cos(s(5)) * C19 * C28) / Jz1 / (cos(s(5)) * C19 * C26 + cos(s(5)) * C20 + 0.1e1);

123 C34 = -(Jz1 * cos(s(5)) * C23 + Jz1 * cos(s(5)) * C19 * C29) / Jz1 / (cos(s(5)) * C19 * C26 + cos(s(5)) * C20 + 0.1e1); C35 = -(Jz1 * cos(s(5)) * C19 * C30 + Jz1 * cos(s(5)) * C24) / Jz1 / (cos(s(5)) * C19 * C26 + cos(s(5)) * C20 + 0.1e1); C36 = -(-Jx1 * s(17) * cos(s(6)) ^ 2 * s(16) * sin(s(5)) + Jx1 * s(17) ^ 2 * cos(s(6)) * sin(s(6)) - F6 + Jx1 * s(16) * sin(s(5)) * sin(s(6)) ^ 2 * s(17) + Jz1 * cos(s(5)) * C19 * C31 - Jy1 * s(17) ^ 2 * cos(s(6)) * sin(s(6)) - Jz1 * s(16) * sin(s(5)) * s(17) - Jy1 * s(16) * sin(s(5)) * sin(s(6)) ^ 2 * s(17) + Jy1 * s(16) ^ 2 * sin(s(5)) ^ 2 * sin(s(6)) * cos(s(6)) + Jz1 * cos(s(5)) * C25 - Jx1 * s(16) ^ 2 * sin(s(5)) ^ 2 * sin(s(6)) * cos(s(6)) + Jy1 * s(17) * cos(s(6)) ^ 2 * s(16) * sin(s(5))) / Jz1 / (cos(s(5)) * C19 * C26 + cos(s(5)) * C20 + 0.1e1); %EQ 7 C37 = -(0.4e1 * Jy2 * cos(s(9)) * sin(s(8)) * sin(s(9)) - 0.4e1 * Jx2 * sin(s(9)) * sin(s(8)) * cos(s(9)) + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C28 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C33 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C22 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C33 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C22 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C33 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C28 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C33 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C33 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C28 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C33 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C28 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C22 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C28 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C33 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C22 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C22 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C28 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C22 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C33 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C28 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C4 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C11 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C28 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C28 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C4 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C33 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C33 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C28 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C11) / (-m1 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m1 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(8)) ^ 2 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 *

124 sin(s(5)) * cos(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C3 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) ^ 2 - 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) ^ 2 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C3 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32); C38 = 0.4e1 * Jz2 * cos(s(8)) / (-m1 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m1 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(8)) ^ 2 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(8))

125 * cos(s(7)) * l2 * C3 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) ^ 2 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) ^ 2 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C3 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32); C39 = -(m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C29 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C23 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C23 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C34 - m3 * sin(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * sin(s(10)) - m3 * sin(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * cos(s(10)) - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C29 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C29 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C34 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C34 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C34 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C29 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C34 m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C34 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C29 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C5 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C34 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C29 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C34 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C23 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C34 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C34 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C23 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C29 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C34 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C23 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C29 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C12 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C34 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C34 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C5 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C23 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C34 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C12) / (-m1 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 -

126 m1 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(8)) ^ 2 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C3 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) ^ 2 - 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) ^ 2 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C3 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32); C40 = -(m3 * sin(s(8)) * sin(s(7)) * l2 * l3 * cos(s(11)) * cos(s(10)) - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C35 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C35 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C35 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C30 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C35 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C24 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C30 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C35 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C24 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C30 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C35 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C30 - m3 * sin(s(8)) * cos(s(7)) * l2 * l3 * cos(s(11)) * sin(s(10)) - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C30 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C30 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C30 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C30 +

127 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C24 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C13 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C35 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C35 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C35 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C30 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C13 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C6 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C30 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C6 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C24 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C24 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C30 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C30 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C35 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C24 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C35 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C35) / (-m1 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 m1 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(8)) ^ 2 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C3 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) ^ 2 - 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) ^ 2 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 *

128 C3 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32); C41 = -(0.4e1 * Jz2 * sin(s(8)) * s(20) * s(21) + (4 * F7) - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * s(17) ^ 2 * cos(s(4)) m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C31 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C36 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C36 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C31 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C25 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C36 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C36 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * s(16) ^ 2 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C31 - m3 * sin(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * cos(s(10)) * s(22) ^ 2 + m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * s(17) ^ 2 * sin(s(4)) m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C25 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C36 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C31 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C36 + m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * s(16) ^ 2 - m3 * sin(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * s(23) ^ 2 * cos(s(10)) + m3 * sin(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * sin(s(10)) * s(22) ^ 2 + m3 * sin(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * s(23) ^ 2 * sin(s(10)) - 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * s(17) * cos(s(4)) * s(16) - 0.8e1 * Jx2 * sin(s(9)) * sin(s(8)) ^ 2 * s(19) * cos(s(9)) * s(21) - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * l3 * cos(s(11)) * s(23) * sin(s(10)) * s(22) - 0.2e1 * m1 * sin(s(8)) * sin(s(7)) ^ 2 * s(19) * l2 ^ 2 * cos(s(8)) * s(20) - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) ^ 2 * l2 ^ 2 * cos(s(8)) * s(20) * s(19) - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) ^ 2 * s(19) * l2 ^ 2 * cos(s(8)) * s(20) + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C25 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C31 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C36 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C31 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C31 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C7 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C25 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C31 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C36 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C7 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C36 - 0.2e1 * m1 * sin(s(8)) * cos(s(7)) ^ 2 * l2 ^ 2 * cos(s(8)) * s(20) * s(19) + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C31 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C25 + 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) * s(20) * s(21) + 0.8e1 * Jz2 * cos(s(8)) * s(19) * sin(s(8)) * s(20) + 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) * s(20) * s(21) - 0.4e1 * Jx2 * cos(s(9)) ^ 2 * s(21) * sin(s(8)) * s(20) - 0.4e1 * Jy2 * sin(s(9)) ^ 2 * s(21) * sin(s(8)) * s(20) + 0.4e1 * Jy2 * cos(s(9)) * cos(s(8)) * s(20) ^ 2 * sin(s(9)) - 0.8e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) * s(19) * cos(s(8)) * s(20) - 0.8e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) * s(19) * cos(s(8)) * s(20) + 0.8e1 * Jy2 * cos(s(9)) * sin(s(8)) ^ 2 * s(19) *

129 sin(s(9)) * s(21) - 0.4e1 * Jx2 * sin(s(9)) * cos(s(8)) * s(20) ^ 2 * cos(s(9)) - 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * s(17) * sin(s(4)) * s(16) - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * l3 * cos(s(11)) * s(23) * cos(s(10)) * s(22) + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C36 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C14 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C14 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C31 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C25) / (-m1 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 - m1 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - m3 * sin(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(8)) ^ 2 m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 - m1 * sin(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 + m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 - m1 * sin(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C10 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C3 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 0.4e1 * Jy2 * cos(s(9)) ^ 2 * sin(s(8)) ^ 2 - 0.4e1 * Jx2 * sin(s(9)) ^ 2 * sin(s(8)) ^ 2 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C26 * C32 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C3 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(8)) * cos(s(7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(8)) * sin(s(7)) * l2 * C9 * C26 * C32); %EQ 8 C42 = -(m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C38 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C38 - m1 * cos(s(8)) * cos(s(7)) *

130 l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C38 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C38 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C38 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C38 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C38 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C38 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C38 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C38 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C38 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C38 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C38 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C38 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C38 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C38 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C38 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C38 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C38 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C38 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C38 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C38 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C38 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C38 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C38) / (m3 * sin(s(8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(9)) ^ 2 + 0.4e1 * Jy2 * sin(s(9)) ^ 2 + m1 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m1 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(8)) * l2 * C16 - 0.2e1 * m3 * sin(s(8)) * l2 * C16 + m1 * sin(s(8)) ^ 2 * l2 ^ 2 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C22 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C22 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C28 + m1 * cos(s(8)) * cos(s(7)) *

131 l2 * l1 * cos(s(5)) * cos(s(4)) * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C33 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C33 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C37 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C37 - 0.2e1 * m1 * cos(s(8)) *

132 sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C11 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37); C43 = -(m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C29 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C39 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C39 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C39 + m3 * cos(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * cos(s(10)) + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C39 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C23 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C39 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C34 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C34 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C39 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C34 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C34 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C29 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C29 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C39 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C34 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C34 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C34 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C23 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C39 - m3 * cos(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * sin(s(10)) + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C39 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C39 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C39 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C29 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C39 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C39 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C29 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C34 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C29 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C39 - 0.2e1 * m1 * cos(s(8)) *

133 sin(s(7)) * l2 * C1 * C20 * C34 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C5 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C29 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C34 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C34 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C39 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C5 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C34 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C39 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C23 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C23 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C12 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C29 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C34 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C39 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C29 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C34 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C29 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C29 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C23 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C39 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C39 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C34 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C12 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C39 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C34 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C34 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C39 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C39 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C39 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C23 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C39 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C34 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C29 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C39 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C39 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C29) / (m3 * sin(s(8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(9)) ^ 2 + 0.4e1 * Jy2 * sin(s(9)) ^ 2 + m1 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m1 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(8)) * l2 * C16 - 0.2e1 * m3 * sin(s(8)) * l2 * C16 + m1 * sin(s(8)) ^ 2 * l2 ^ 2 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C22 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C22 + m1 *

134 cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C28 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C33 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C33 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 *

135 C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C37 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C11 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37); C44 = -(-0.2e1 * m3 * sin(s(8)) * l2 * C17 + 0.2e1 * m1 * sin(s(8)) * l2 * C17 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C40 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C35 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C40 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C40 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C30 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C30 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C40 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C40 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C40 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C30 + m3 * cos(s(8)) * cos(s(7)) * l2 * l3 * cos(s(11)) * cos(s(10)) - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C24 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C35 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C40 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C35 + m3 * cos(s(8)) * sin(s(7)) * l2 * l3 * cos(s(11)) * sin(s(10)) + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C35 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C30 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C40 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C40 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C30 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C40 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C24 + m3 * sin(s(8)) * l2 * sin(s(11)) * l3 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C35 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C40 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C35 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C40 m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C35 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) *

136 sin(s(4)) * C19 * C27 * C40 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C40 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C13 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C30 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C30 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C24 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C30 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C35 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C6 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C30 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C13 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C24 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C30 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C6 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C35 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C40 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C35 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C24 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C40 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C24 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C30 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C30 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C30 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C40 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C40 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C35) / (m3 * sin(s(8)) ^ 2 * l2

137 ^ 2 + 0.4e1 * Jx2 * cos(s(9)) ^ 2 + 0.4e1 * Jy2 * sin(s(9)) ^ 2 + m1 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m1 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(8)) * l2 * C16 - 0.2e1 * m3 * sin(s(8)) * l2 * C16 + m1 * sin(s(8)) ^ 2 * l2 ^ 2 m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C22 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C22 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C28 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C33 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C33 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 -

138 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C37 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C11 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37); C45 = -(-0.2e1 * m3 * g * sin(s(8)) * l2 + 0.2e1 * m1 * sin(s(8)) * l2 * C18 - 0.2e1 * m3 * sin(s(8)) * l2 * C18 + 0.2e1 * m1 * g * sin(s(8)) * l2 + 0.4e1 * Jz2 * s(19) ^ 2 * sin(s(8)) * cos(s(8)) + 0.4e1 * Jz2 * s(19) * sin(s(8)) * s(21) - (4 * F8) + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C31 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C31 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C36 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C41 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C36 m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C41 - m3 * cos(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * cos(s(10)) * s(22) ^ 2 - m3 * cos(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * sin(s(10)) * s(22) ^ 2 + m1 * sin(s(8)) * l2 * cos(s(5)) * s(17) ^ 2 * l1 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C41 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C36 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C41 - m3 * cos(s(8)) * cos(s(7)) * l2 * l3 * sin(s(11)) * s(23) ^ 2 * cos(s(10)) + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C41 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C41 - m3 * cos(s(8)) * sin(s(7)) * l2 * l3 * sin(s(11)) * s(23) ^ 2 * sin(s(10)) + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C41 - m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * s(16) ^ 2 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * s(16) ^ 2 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 *

139 sin(s(5)) * sin(s(4)) * C25 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C31 + m3 * sin(s(8)) * l2 ^ 2 * cos(s(8)) * s(20) ^ 2 + m3 * sin(s(8)) * l2 * cos(s(11)) * s(23) ^ 2 * l3 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C31 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C41 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C41 - m3 * cos(s(8)) * cos(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(20) ^ 2 - m1 * cos(s(8)) * sin(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(20) ^ 2 - m3 * cos(s(8)) * sin(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(20) ^ 2 m1 * cos(s(8)) * cos(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(20) ^ 2 - m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * s(17) ^ 2 * sin(s(4)) m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * s(17) ^ 2 * cos(s(4)) - m1 * cos(s(8)) * cos(s(7)) ^ 2 * s(19) ^ 2 * l2 ^ 2 * sin(s(8)) - m1 * cos(s(8)) * sin(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(19) ^ 2 - m3 * cos(s(8)) * cos(s(7)) ^ 2 * s(19) ^ 2 * l2 ^ 2 * sin(s(8)) m3 * cos(s(8)) * sin(s(7)) ^ 2 * l2 ^ 2 * sin(s(8)) * s(19) ^ 2 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C31 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C41 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C36 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C41 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C41 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C36 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C36 + m1 * sin(s(8)) * l2 ^ 2 * cos(s(8)) * s(20) ^ 2 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C41 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C36 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C41 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C25 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * l3 * cos(s(11)) * s(23) * sin(s(10)) * s(22) - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C7 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C14 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C31 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C25 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C36 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C25 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C25 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C31 - 0.4e1 * Jy2 * s(19) ^ 2 * cos(s(8)) * cos(s(9)) ^ 2 * sin(s(8)) + 0.4e1 * Jx2 * cos(s(9)) ^ 2 * s(19) * sin(s(8)) * s(21) + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C36 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C36 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C31 + 0.4e1 * Jy2 * sin(s(9)) ^ 2 * s(19) * sin(s(8)) * s(21) + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * l3 * cos(s(11)) * s(23) * cos(s(10)) * s(22) - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 *

140 cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C36 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C41 + 0.8e1 * Jy2 * sin(s(9)) * s(20) * cos(s(9)) * s(21) - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C31 + 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * s(17) * cos(s(4)) * s(16) - 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * s(17) * sin(s(4)) * s(16) + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C31 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C31 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C36 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C36 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C41 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C41 - 0.4e1 * Jx2 * sin(s(9)) ^ 2 * s(21) * s(19) * sin(s(8)) - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C41 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C41 - 0.4e1 * Jx2 * s(19) ^ 2 * cos(s(8)) * sin(s(9)) ^ 2 * sin(s(8)) - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C14 - 0.8e1 * Jx2 * cos(s(9)) * s(20) * sin(s(9)) * s(21) - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C31 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C31 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C36 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C41 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C31 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C36 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C41 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C7 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C41 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C25 - 0.4e1 * Jy2 * cos(s(9)) ^ 2 * s(21) * s(19) * sin(s(8)) - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C36 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C41 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C41 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C41) / (m3 * sin(s(8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(9)) ^ 2 + 0.4e1 * Jy2 * sin(s(9)) ^ 2 + m1 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m1 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * cos(s(7)) ^ 2 * l2 ^ 2 + m3 * cos(s(8)) ^ 2 * sin(s(7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(8)) * l2 * C16 - 0.2e1 * m3 * sin(s(8)) * l2 * C16 + m1 * sin(s(8)) ^ 2 * l2 ^ 2 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C22 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C22 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C28 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C28 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C33 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C33 - m1 * cos(s(8)) *

141 cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C21 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C27 * C37 + m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * cos(s(5)) * cos(s(4)) * C26 * C32 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C27 * C37 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C33 + m1 * sin(s(8)) * l2 * sin(s(5)) * l1 * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * cos(s(5)) * sin(s(4)) * C26 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C20 * C32 * C37 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C26 * C33 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C20 * C32 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C19 * C28 - m1 * cos(s(8)) * cos(s(7)) * l2 * l1 * sin(s(5)) * sin(s(4)) * C19 * C27 * C37 + m1 * cos(s(8)) * sin(s(7)) * l2 * l1 * sin(s(5)) * cos(s(4)) * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C4 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(9)) * sin(s(8)) * sin(s(9)) * C37 - 0.4e1 * Jy2 * sin(s(9)) * sin(s(8)) * cos(s(9)) * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 *

142 C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(8)) * cos(s(7)) * l2 * C11 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C27 * C37 - 0.2e1 * m1 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(8)) * cos(s(7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(8)) * sin(s(7)) * l2 * C1 * C19 * C27 * C37); %EQ 9 C46 = (-Jz2 * cos(s(8)) * C37 * C43 - Jz2 * cos(s(8)) * C39) / Jz2 / (cos(s(8)) * C37 * C42 + cos(s(8)) * C38 + 0.1e1); C47 = (-Jz2 * cos(s(8)) * C40 - Jz2 * cos(s(8)) * C37 * C44) / Jz2 / (cos(s(8)) * C37 * C42 + cos(s(8)) * C38 + 0.1e1); C48 = (Jy2 * s(19) * sin(s(8)) * sin(s(9)) ^ 2 * s(20) - Jz2 * cos(s(8)) * C41 - Jz2 * cos(s(8)) * C37 * C45 + Jx2 * s(19) ^ 2 * sin(s(8)) ^ 2 * sin(s(9)) * cos(s(9)) - Jx2 * s(19) * sin(s(8)) * sin(s(9)) ^ 2 * s(20) + Jx2 * s(20) * cos(s(9)) ^ 2 * s(19) * sin(s(8)) + Jz2 * s(19) * sin(s(8)) * s(20) - Jy2 * s(19) ^ 2 * sin(s(8)) ^ 2 * sin(s(9)) * cos(s(9)) - Jy2 * s(20) * cos(s(9)) ^ 2 * s(19) * sin(s(8)) + Jy2 * s(20) ^ 2 * cos(s(9)) * sin(s(9)) - Jx2 * s(20) ^ 2 * cos(s(9)) * sin(s(9)) + F9) / Jz2 / (cos(s(8)) * C37 * C42 + cos(s(8)) * C38 + 0.1e1); %EQ 10 C49 = (0.4e1 * Jy3 * cos(s(12)) * sin(s(11)) * sin(s(12)) - 0.4e1 * Jx3 * sin(s(12)) * sin(s(11)) * cos(s(12)) - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C44 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C40 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C47 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C47 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C47 m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C47 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C40 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C44 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C47 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C47 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C44 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 *

143 sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C44 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C35 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C40 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C6 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C30 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C30 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C40 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C24 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3

144 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C44 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C40 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C30 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C13 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C24 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C30 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C35) / (m3 * sin(s(11)) ^ 2 * sin(s(10)) ^ 2 * l3 ^ 2 + m3 * sin(s(11)) ^ 2 * cos(s(10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(12)) ^ 2 * sin(s(11)) ^ 2 + 0.4e1 * Jz3 * cos(s(11)) ^ 2 + 0.4e1 * Jx3 * sin(s(12)) ^ 2 * sin(s(11)) ^ 2 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 *

145 C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C12 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C5 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27

146 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C39); C50 = -0.4e1 * Jz3 * cos(s(11)) / (m3 * sin(s(11)) ^ 2 * sin(s(10)) ^ 2 * l3 ^ 2 + m3 * sin(s(11)) ^ 2 * cos(s(10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(12)) ^ 2 * sin(s(11)) ^ 2 + 0.4e1 * Jz3 * cos(s(11)) ^ 2 + 0.4e1 * Jx3 * sin(s(12)) ^ 2 * sin(s(11)) ^ 2 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32

147 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C12 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C5 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 *

148 C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C39); C51 = (0.4e1 * Jz3 * sin(s(11)) * s(23) * s(24) + (4 * F10) - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C48 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C45 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C48 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C48 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C45 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C45 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C41 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C48 m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C48 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C48 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C41 - m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C45 - 0.8e1 * Jx3 * sin(s(12)) ^ 2 * sin(s(11)) * s(22) * cos(s(11)) * s(23) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) *

149 sin(s(10)) * l3 * C8 * C20 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C41 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C7 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C48 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C42 * C48 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C45 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C41 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C36 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C36 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C31 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C41 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C41 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C42 * C48 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) ^ 2 * l3 ^ 2 * cos(s(11)) * s(23) * s(22) 0.2e1 * m3 * sin(s(11)) * sin(s(10)) ^ 2 * s(22) * l3 ^ 2 * cos(s(11)) * s(23) - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C41 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C38 * C48 + 0.8e1 * Jz3 * cos(s(11)) * s(22) * sin(s(11)) * s(23) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C14 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32

150 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C45 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C36 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C38 * C48 + 0.4e1 * Jx3 * sin(s(12)) ^ 2 * sin(s(11)) * s(23) * s(24) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C45 0.4e1 * Jx3 * cos(s(12)) ^ 2 * s(24) * sin(s(11)) * s(23) - 0.4e1 * Jy3 * sin(s(12)) ^ 2 * s(24) * sin(s(11)) * s(23) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C42 * C48 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C41 - 0.4e1 * Jx3 * sin(s(12)) * cos(s(11)) * s(23) ^ 2 * cos(s(12)) 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C31 + 0.4e1 * Jy3 * cos(s(12)) * cos(s(11)) * s(23) ^ 2 * sin(s(12)) + 0.4e1 * Jy3 * cos(s(12)) ^ 2 * sin(s(11)) * s(23) * s(24) - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C48 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C41 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C42 * C48 - 0.8e1 * Jx3 * sin(s(12)) * sin(s(11)) ^ 2 * s(22) * cos(s(12)) * s(24) + 0.8e1 * Jy3 * cos(s(12)) * sin(s(11)) ^ 2 * s(22) * sin(s(12)) * s(24) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19) - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C25 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C31 - 0.8e1 * Jy3 * cos(s(12)) ^ 2 * sin(s(11)) * s(22) * cos(s(11)) * s(23) - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C41 - 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C45 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C45 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C25 - 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C41) / (m3 * sin(s(11)) ^ 2 * sin(s(10)) ^ 2 * l3 ^ 2 + m3 * sin(s(11)) ^ 2 * cos(s(10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(12)) ^ 2 * sin(s(11)) ^ 2 + 0.4e1 * Jz3 * cos(s(11)) ^ 2 + 0.4e1 * Jx3 * sin(s(12)) ^ 2 * sin(s(11)) ^ 2 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 + m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 + m3 * sin(s(11)) * sin(s(10))

151 * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 - m3 * sin(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 + m3 * sin(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C12 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20

152 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C5 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C4 * C42 * C46 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C27 * C39 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C8 * C19 * C29 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C1 * C21 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C26 * C34 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C2 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C9 * C28 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C11 * C43 + 0.2e1 * m3 * sin(s(11)) * sin(s(10)) * l3 * C10 * C39 + 0.2e1 * m3 * sin(s(11)) * cos(s(10)) * l3 * C3 * C39); %EQ 11 C52 = (-m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 * C50 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 * C50 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 * C50 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 * C50 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 * C50 m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 * C50 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 * C50 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C43 * C50 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 * C50 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C46 * C50 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 * C50 + m3 * cos(s(11)) * cos(s(10)) * l3 *

153 l2 * sin(s(8)) * sin(s(7)) * C38 * C46 * C50 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 * C50 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C29 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C12 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C5 * C50 + 0.4e1 * Jy3 * sin(s(12)) * sin(s(11)) * cos(s(12)) * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C29 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C43 * C50 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C39 * C50 0.4e1 * Jx3 * cos(s(12)) * sin(s(11)) * sin(s(12)) * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C34 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C29 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C34 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C29 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C43 * C50 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 * C50 + 0.2e1 * m3 *

154 cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C23 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C23 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C50 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C29 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C34 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C43 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C39 * C50 + 0.2e1 * m3 * sin(s(11))

155 * l3 * C15 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C46 * C50) / (m3 * cos(s(11)) ^ 2 * sin(s(10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C17 + m3 * sin(s(11)) ^ 2 * l3 ^ 2 + m3 * cos(s(11)) ^ 2 * cos(s(10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C13 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C44 + 0.4e1 * Jx3 * cos(s(12)) ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C29 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C30 + 0.4e1 * Jx3 * cos(s(12)) * sin(s(11)) * sin(s(12)) * C49 0.4e1 * Jy3 * sin(s(12)) * sin(s(11)) * cos(s(12)) * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C6 + 0.4e1 * Jy3 * sin(s(12)) ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C44 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C47 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C46 * C49 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C44 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C43 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C40 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C44 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C44 m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C47 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C40 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C44 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 * C49 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 * C49 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C47 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 * C49 m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C44 + m3 * cos(s(11)) * sin(s(10)) * l3 *

156 l2 * sin(s(8)) * cos(s(7)) * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C39 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C34 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C40 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C24 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C29 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47

157 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C12 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C24 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C29 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C29 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C29 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C23 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C35 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C47 +

158 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C34 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C23 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C46 * C49

159 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C5 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C40); C53 = (0.2e1 * m3 * g * sin(s(11)) * l3 + 0.4e1 * Jx3 * s(22) ^ 2 * cos(s(11)) * sin(s(12)) ^ 2 * sin(s(11)) + 0.4e1 * Jy3 * s(22) ^ 2 * cos(s(11)) * cos(s(12)) ^ 2 * sin(s(11)) + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C14 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C5 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C39 * C51 - 0.4e1 * Jz3 * s(22) * sin(s(11)) * s(24) - 0.8e1 * Jy3 * sin(s(12)) * s(23) * cos(s(12)) * s(24) + 0.2e1 * m3 * sin(s(11)) * l3 * C18 - 0.4e1 * Jz3 * s(22) ^ 2 * sin(s(11)) * cos(s(11)) + 0.8e1 * Jx3 * cos(s(12)) * s(23) * sin(s(12)) * s(24) + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C34 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C7 + (4 * F11) - m3 * sin(s(11)) * l3 * cos(s(8)) * s(20) ^ 2 * l2 - m3 * sin(s(11)) * l3 ^ 2 * cos(s(11)) * s(23) ^ 2 + m3 * cos(s(11)) * sin(s(10)) ^ 2 * l3 ^ 2 * sin(s(11)) * s(23) ^ 2 + m3 * cos(s(11)) * cos(s(10)) ^ 2 * l3 ^ 2 * sin(s(11)) * s(23) ^ 2 + m3 * cos(s(11)) * cos(s(10)) ^ 2 * s(22) ^

160 2 * l3 ^ 2 * sin(s(11)) + m3 * cos(s(11)) * sin(s(10)) ^ 2 * l3 ^ 2 * sin(s(11)) * s(22) ^ 2 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C46 * C51 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C48 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C43 * C51 - m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C45 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * s(20) ^ 2 * cos(s(7)) - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C41 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * s(20) ^ 2 * sin(s(7)) + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * s(19) ^ 2 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C45 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 * C51 m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C48 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C45 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C41 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 * C51 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C48 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 * C51 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C48 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 * C51 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C48 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C45 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C48 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 * C51 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C48 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C45 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 * C51 - m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 * C51 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * s(19) ^ 2 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C31 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 * C51 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C41 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C34 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C46 * C51 0.4e1 * Jy3 * sin(s(12)) ^ 2 * s(22) * sin(s(11)) * s(24) + 0.4e1 * Jy3 * cos(s(12)) ^ 2 * s(24) * s(22) * sin(s(11)) + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C31 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C43 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C48 + 0.2e1 * m3 *

161 sin(s(11)) * l3 * C15 * C27 * C38 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C45 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C39 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C29 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C36 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C43 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C45 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C45 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C45 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C41 + 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C43 * C51 + 0.4e1 * Jy3 * sin(s(12)) * sin(s(11)) * cos(s(12)) * C51 - 0.4e1 * Jx3 * cos(s(12)) * sin(s(11)) * sin(s(12)) * C51 - 0.4e1 * Jx3 * cos(s(12)) ^ 2 * s(22) * sin(s(11)) * s(24) + 0.4e1 * Jx3 * sin(s(12)) ^ 2 * s(24) * s(22) * sin(s(11)) - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C25 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C25 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C36 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C36 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C39 * C51 - 0.2e1 * m3 *

162 cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C39 * C51 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C48 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C41 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C34 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C31 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C36 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C34 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 * C51

163 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C12 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C34 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C29 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C31 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C31 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C23 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C34 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C29 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C36 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C23 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C29 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C51 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C45 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C34 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27

164 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C39 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C48 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C29 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C41 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C36 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C45 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C45 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C43 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C39 * C51 - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * s(20) * sin(s(7)) * s(19) - 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * s(20) * cos(s(7)) * s(19)) / (m3 * cos(s(11)) ^ 2 * sin(s(10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C17 + m3 * sin(s(11)) ^ 2 * l3 ^ 2 + m3 * cos(s(11)) ^ 2 * cos(s(10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C13 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C40 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C47 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C44 + 0.4e1 * Jx3 * cos(s(12)) ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C29 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C43 * C49 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C30 + 0.4e1 * Jx3 * cos(s(12)) * sin(s(11)) * sin(s(12)) * C49 0.4e1 * Jy3 * sin(s(12)) * sin(s(11)) * cos(s(12)) * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C6 + 0.4e1 * Jy3 * sin(s(12)) ^ 2 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C44 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 *

165 C42 * C47 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C42 * C46 * C49 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C44 + m3 * sin(s(11)) * l3 * sin(s(8)) * l2 * C43 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C40 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C46 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C44 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C44 m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C47 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C40 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C44 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C42 * C46 * C49 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C46 * C49 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C42 * C47 + m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * cos(s(8)) * cos(s(7)) * C43 * C49 m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C39 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C37 * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C46 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * cos(s(8)) * sin(s(7)) * C42 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C39 * C49 - m3 * cos(s(11)) * cos(s(10)) * l3 * l2 * sin(s(8)) * sin(s(7)) * C38 * C46 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C42 * C47 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C43 * C49 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C37 * C44 + m3 * cos(s(11)) * sin(s(10)) * l3 * l2 * sin(s(8)) * cos(s(7)) * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C39 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(11)) * l3 * C16 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C34 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C28 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26

166 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C40 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C24 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C29 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C12 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C42 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C44 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C24 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C29 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C29 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 *

167 cos(s(11)) * cos(s(10)) * l3 * C11 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C29 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C23 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C39 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C22 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C35 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1

168 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C11 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C39 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C47 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C30 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C34 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C40 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C23 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C10 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C5 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C3 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C4 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C49 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C42

169 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C20 * C35 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(11)) * cos(s(10)) * l3 * C9 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(11)) * sin(s(10)) * l3 * C2 * C26 * C32 * C40); %EQ 12 C54 = (-Jz3 * cos(s(11)) * C49 * C53 - Jz3 * cos(s(11)) * C51 + Jz3 * s(22) * sin(s(11)) * s(23) + Jx3 * s(22) ^ 2 * sin(s(11)) ^ 2 * sin(s(12)) * cos(s(12)) - Jx3 * s(22) * sin(s(11)) * sin(s(12)) ^ 2 * s(23) + Jx3 * s(23) * cos(s(12)) ^ 2 * s(22) * sin(s(11)) - Jx3 * s(23) ^ 2 * cos(s(12)) * sin(s(12)) - Jy3 * s(22) ^ 2 * sin(s(11)) ^ 2 * sin(s(12)) * cos(s(12)) - Jy3 * s(23) * cos(s(12)) ^ 2 * s(22) * sin(s(11)) + Jy3 * s(22) * sin(s(11)) * sin(s(12)) ^ 2 * s(23) + Jy3 * s(23) ^ 2 * cos(s(12)) * sin(s(12)) + F12) / Jz3 / (cos(s(11)) * C49 * C52 + cos(s(11)) * C50 + 0.1e1);

Control Torques – Ts.m %This script file contains the generalized forces which were inserted as placeholders in the algebraic section. %Read the PD Gains Constants; %Generalized Forces F1 = 0; F2 = 0; F3 = 0; F4 = KX1 * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + KY1 * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + KZ1 * sin(s(5)) * cos(s(4)) * sin(s(8)) * sin(s(7)) + JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + KY1 * sin(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(18) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(21) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(19) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - JX1 * s(18) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(18) * cos(s(6)) * cos(s(4)) * sin(s(9)) *

170 sin(s(7)) + JY1 * s(21) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(6)) * cos(s(5)) * sin(s(4)) + JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - KY1 * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - JX1 * s(18) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + KY1 * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - KX1 * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + JY1 * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(19) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) JX1 * s(18) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JX1 * s(16) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + JX1 * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(16) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(21) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + JX1 * s(21) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + KX1 * cos(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + JX1 * s(19) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(19) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(21) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JX1 * s(18) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(19) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - KX1 * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - KZ1 * d13 - JX1 * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(6)) * cos(s(5)) * sin(s(4)) + JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JX1 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(6)) * cos(s(5)) * cos(s(4)) - JX1 * s(16) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(19) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(16) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - KY1 * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - KY1 * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JZ1 * s(16) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) - JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(6)) * cos(s(4)) - JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(21) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - JX1 * s(18) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(21) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JZ1 * s(20) * sin(s(5)) * cos(s(4)) * cos(s(8)) * sin(s(7)) + JZ1 * s(19) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) + JZ1 * s(19) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) + JZ1 * s(17) * cos(s(5)) * cos(s(4)) * sin(s(8)) * sin(s(7)) + JX1 * s(19) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + KX1 * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + KY1 * cos(s(6)) * cos(s(5)) *

171 cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JX1 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(6)) * sin(s(4)) + KX1 * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(21) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - JY1 * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - JY1 * s(18) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) JY1 * s(18) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - JY1 * s(18) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(18) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - JY1 * s(18) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(21) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(21) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + JY1 * s(21) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(21) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - JY1 * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(19) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(6)) * sin(s(4)) + JY1 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(6)) * cos(s(4)) - KX1 * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + JY1 * s(21) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(16) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(16) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - JY1 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(6)) * cos(s(5)) * cos(s(4)) + JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(18) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(16) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JX1 * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - JX1 * s(18) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - KY1 * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JX1 * s(21) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - JY1 * s(18) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(16) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + JX1 * s(21) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JX1 * s(18) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - KX1 * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - JZ1 * s(20) * sin(s(5)) * sin(s(4)) * cos(s(8)) * cos(s(7)) - JZ1 * s(17) * cos(s(5)) * sin(s(4)) * sin(s(8)) * cos(s(7)) - JZ1 * s(16) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) - KZ1 * sin(s(5)) * sin(s(4)) * sin(s(8)) * cos(s(7)) - JY1 * s(21) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)); F5 = sin(s(4)) * JZ1 * s(20) * cos(s(5)) * cos(s(8)) * sin(s(7)) + sin(s(4)) * JZ1 * cos(s(5)) * sin(s(8)) * cos(s(7)) * s(19) - sin(s(4)) * KX1 * sin(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + KY1 * cos(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) - JZ1 * s(17) * cos(s(5)) * cos(s(8)) + JZ1 * s(20) * sin(s(5)) * sin(s(8)) - sin(s(4)) * JY1 * s(17) * cos(s(6)) * cos(s(5)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(4)) * JY1 * s(17) * cos(s(6)) * cos(s(5)) * sin(s(9)) * cos(s(7)) - sin(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(7)) - sin(s(4)) * JX1 * sin(s(6)) * sin(s(5)) * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(4)) * JX1 * sin(s(6)) * sin(s(5)) * s(19) * cos(s(9)) * sin(s(7)) - sin(s(4)) *

172 JX1 * s(18) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(4)) * JX1 * s(17) * sin(s(6)) * cos(s(5)) * cos(s(9)) * cos(s(7)) - JY1 * s(18) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) + JY1 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(6)) * cos(s(5)) - JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(8)) - cos(s(4)) * JX1 * s(18) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * cos(s(7)) cos(s(4)) * JX1 * s(18) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(7)) - cos(s(4)) * JX1 * s(17) * sin(s(6)) * cos(s(5)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(4)) * JX1 * s(17) * sin(s(6)) * cos(s(5)) * cos(s(9)) * sin(s(7)) - JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(8)) + sin(s(4)) * JY1 * s(18) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(7)) + JX1 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) + cos(s(4)) * JY1 * cos(s(6)) * sin(s(5)) * s(19) * sin(s(9)) * cos(s(7)) + cos(s(4)) * JY1 * s(17) * cos(s(6)) * cos(s(5)) * sin(s(9)) * sin(s(7)) + sin(s(4)) * JY1 * cos(s(6)) * sin(s(5)) * s(19) * sin(s(9)) * sin(s(7)) - cos(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + sin(s(4)) * JX1 * s(18) * cos(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(7)) - cos(s(4)) * KY1 * cos(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(4)) * KX1 * sin(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(4)) * JX1 * sin(s(6)) * sin(s(5)) * s(19) * cos(s(9)) * cos(s(7)) + sin(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(4)) * KX1 * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(7)) + sin(s(4)) * JY1 * s(20) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(8)) * sin(s(7)) + cos(s(4)) * JY1 * s(18) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(4)) * JY1 * cos(s(6)) * sin(s(5)) * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * JX1 * s(20) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(8)) * cos(s(7)) + cos(s(4)) * JX1 * sin(s(6)) * sin(s(5)) * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * JZ1 * s(20) * cos(s(5)) * cos(s(8)) * cos(s(7)) + JX1 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(6)) * cos(s(5)) - JY1 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) + sin(s(4)) * JX1 * s(20) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(8)) * sin(s(7)) - JY1 * cos(s(9)) * sin(s(8)) * s(16) * sin(s(6)) - sin(s(4)) * JX1 * s(17) * sin(s(6)) * cos(s(5)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * KY1 * cos(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(7)) + cos(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(7)) + JX1 * sin(s(9)) * sin(s(8)) * s(16) * cos(s(6)) - sin(s(4)) * JY1 * cos(s(6)) * sin(s(5)) * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(4)) * JY1 * s(20) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(8)) * cos(s(7)) + KX1 * sin(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) - sin(s(4)) * KY1 * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(7)) - sin(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(7)) + JX1 * s(18) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) - sin(s(4)) * KY1 * cos(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(4)) * KX1 * sin(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(7)) cos(s(4)) * JZ1 * cos(s(5)) * sin(s(8)) * sin(s(7)) * s(19) + sin(s(4)) * KZ1 * cos(s(5)) * sin(s(8)) * sin(s(7)) - cos(s(4)) * JY1 * s(17) * cos(s(6)) * cos(s(5)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(4)) * JZ1 * s(17) * sin(s(5)) * sin(s(8)) * sin(s(7)) + cos(s(4)) * KZ1 * cos(s(5)) * sin(s(8)) * cos(s(7)) - cos(s(4)) * JY1 * s(18) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(7)) - cos(s(4)) * JZ1 * s(17) * sin(s(5)) * sin(s(8)) * cos(s(7)) + sin(s(4)) * JY1 * s(18) * sin(s(6))

173 * sin(s(5)) * sin(s(9)) * cos(s(7)) - sin(s(4)) * KZ1 * d12 - cos(s(4)) * KZ1 * d11 - KZ1 * sin(s(5)) * cos(s(8)); F6 = cos(s(5)) * JY1 * s(16) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(5)) * JX1 * s(21) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(5)) * JX1 * s(21) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(5)) ^ 2 * JY1 * s(16) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(5)) * JY1 * s(18) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(5)) * JY1 * s(19) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(5)) * JY1 * s(19) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + sin(s(5)) * JY1 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(6)) + sin(s(4)) * JY1 * s(21) * cos(s(6)) * cos(s(9)) * sin(s(7)) cos(s(5)) * JX1 * s(18) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(5)) * sin(s(4)) * KZ1 * d11 + sin(s(5)) * cos(s(4)) * KZ1 * d12 - JZ1 * cos(s(8)) * s(16) * cos(s(5)) ^ 2 + sin(s(5)) * JX1 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(6)) + cos(s(5)) * KY1 * sin(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(5)) * JX1 * s(21) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(5)) * KX1 * cos(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(5)) * JX1 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(6)) * sin(s(4)) + cos(s(4)) * KY1 * cos(s(6)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * JY1 * s(21) * cos(s(6)) * cos(s(9)) * cos(s(7)) - cos(s(5)) * JX1 * s(16) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * JX1 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(6)) * cos(s(4)) + cos(s(4)) * JX1 * sin(s(6)) * s(19) * cos(s(9)) * sin(s(7)) cos(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(4)) * KX1 * sin(s(6)) * cos(s(9)) * cos(s(7)) - sin(s(5)) * KY1 * cos(s(9)) * sin(s(8)) * sin(s(6)) - cos(s(5)) ^ 2 * JX1 * s(16) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(4)) * JX1 * sin(s(6)) * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(5)) * JY1 * s(16) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + sin(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(9)) * sin(s(7)) + sin(s(5)) * JX1 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(6)) + cos(s(4)) * JX1 * s(21) * sin(s(6)) * sin(s(9)) * cos(s(7)) - cos(s(5)) * JY1 * s(16) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + sin(s(5)) * KX1 * sin(s(9)) * sin(s(8)) * cos(s(6)) - cos(s(5)) * JY1 * s(18) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(5)) * JY1 * s(18) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(4)) * JZ1 * s(17) * sin(s(8)) * sin(s(7)) - cos(s(5)) ^ 2 * JY1 * s(16) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) cos(s(5)) * JY1 * s(16) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(5)) ^ 2 * JY1 * s(16) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * JY1 * s(19) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + sin(s(4)) * JY1 * cos(s(6)) * s(19) * sin(s(9)) * cos(s(7)) - cos(s(5)) ^ 2 * JX1 * s(16) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(5)) * JY1 * s(19) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(4)) * JX1 * s(18) * cos(s(6)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(4)) * KX1 * sin(s(6)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(4)) * JX1 * s(20) * sin(s(6)) * sin(s(9)) * sin(s(8)) * cos(s(7)) + cos(s(4)) * JX1 * sin(s(6)) * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) ^ 2 * JY1 * s(16) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - sin(s(4)) * JX1 * s(18) * cos(s(6)) * cos(s(9)) * sin(s(7)) - cos(s(5)) * JY1 * s(21) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(4)) * JX1 * s(18) * cos(s(6)) * cos(s(9)) * cos(s(7)) + cos(s(4)) * KY1 * cos(s(6)) * sin(s(9)) * cos(s(7)) -

174 sin(s(4)) * JY1 * s(18) * sin(s(6)) * sin(s(9)) * sin(s(7)) - sin(s(5)) * JY1 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(6)) + cos(s(5)) * KX1 * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(5)) * KX1 * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) cos(s(4)) * JY1 * s(18) * sin(s(6)) * sin(s(9)) * cos(s(7)) - sin(s(5)) * JY1 * s(18) * cos(s(9)) * sin(s(8)) * cos(s(6)) - cos(s(4)) * JX1 * s(20) * sin(s(6)) * sin(s(9)) * sin(s(8)) * sin(s(7)) - sin(s(4)) * JX1 * sin(s(6)) * s(19) * cos(s(9)) * cos(s(7)) - cos(s(5)) * KX1 * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - sin(s(4)) * JZ1 * s(17) * sin(s(8)) * cos(s(7)) - cos(s(5)) * KY1 * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + sin(s(4)) * JY1 * s(20) * cos(s(6)) * cos(s(9)) * sin(s(8)) * cos(s(7)) + cos(s(5)) * JX1 * s(21) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + sin(s(4)) * JY1 * cos(s(6)) * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(5)) * JX1 * s(18) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(5)) * JZ1 * s(16) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) + cos(s(4)) * JX1 * s(21) * sin(s(6)) * cos(s(9)) * cos(s(8)) * sin(s(7)) cos(s(5)) * KY1 * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * JZ1 * s(16) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) - cos(s(5)) * JX1 * s(18) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) ^ 2 * JX1 * s(16) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(4)) * JY1 * cos(s(6)) * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(4)) * KX1 * sin(s(6)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * JX1 * s(16) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(4)) * JY1 * cos(s(6)) * s(19) * sin(s(9)) * sin(s(7)) + sin(s(4)) * KY1 * cos(s(6)) * sin(s(9)) * sin(s(7)) + cos(s(5)) * JY1 * s(21) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + sin(s(4)) * JY1 * s(21) * cos(s(6)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + sin(s(4)) * JY1 * s(18) * sin(s(6)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(5)) * JX1 * sin(s(9)) * sin(s(8)) * s(16) * sin(s(6)) * cos(s(5)) - sin(s(4)) * KY1 * cos(s(6)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(5)) * JX1 * s(18) * sin(s(9)) * sin(s(8)) * sin(s(6)) + cos(s(5)) * JX1 * s(19) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(5)) * JY1 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(6)) * cos(s(4)) + cos(s(5)) * JX1 * s(19) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(5)) * JX1 * s(18) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(5)) ^ 2 * JX1 * s(16) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(5)) * JY1 * s(18) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - cos(s(4)) * JY1 * s(20) * cos(s(6)) * cos(s(9)) * sin(s(8)) * sin(s(7)) - cos(s(4)) * JY1 * s(18) * sin(s(6)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(5)) * JY1 * cos(s(9)) * sin(s(8)) * s(16) * cos(s(6)) * cos(s(5)) - sin(s(4)) * JX1 * s(18) * cos(s(6)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * JX1 * s(19) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(5)) * JY1 * s(21) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(5)) * JY1 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(6)) * sin(s(4)) + cos(s(5)) * JY1 * s(21) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(5)) * KY1 * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(5)) * JX1 * s(19) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(5)) * JX1 * s(16) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(4)) * KX1 * sin(s(6)) * cos(s(9)) * sin(s(7)) cos(s(5)) * JX1 * s(16) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - sin(s(4)) * JX1 * s(21) * sin(s(6)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(5)) * KZ1 * d13 + JZ1 * cos(s(8)) * s(16);

175 F7 = JZ3 * s(20) * cos(s(8)) * sin(s(7)) * sin(s(11)) * cos(s(10)) JX3 * s(23) * sin(s(12)) * sin(s(11)) * cos(s(10)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JZ3 * s(19) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) + JZ3 * s(19) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) - JY3 * s(22) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - KY3 * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + KX3 * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JX3 * s(19) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(24) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(22) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(19) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(24) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(24) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + JY3 * s(23) * cos(s(12)) * sin(s(11)) * sin(s(10)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JX3 * s(21) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(21) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + JX3 * s(22) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(21) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(23) * cos(s(12)) * sin(s(11)) * cos(s(10)) * sin(s(9)) * cos(s(7)) JY3 * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - JY3 * s(24) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(22) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - JX3 * s(22) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(22) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + JX3 * s(24) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - KX1 * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - KY1 * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - KZ1 * sin(s(5)) * cos(s(4)) * sin(s(8)) * sin(s(7)) - JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - KY1 * sin(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - JX1 * s(18) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) JX1 * s(21) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(19) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + JX1 * s(18) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + JX3 * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JY3 * s(21) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - KX3 * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - KY3 * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - KY3 * sin(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) JY1 * s(18) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - JY1 *

176 s(21) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + KY1 * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + JX1 * s(18) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - KY1 * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + KX1 * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - JY1 * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(19) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(18) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JX1 * s(16) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - JX1 * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(16) * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JX1 * s(21) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - JX1 * s(21) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - KX1 * cos(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - JX1 * s(19) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(19) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(21) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) JX1 * s(18) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(19) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + KX1 * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + KZ1 * d13 - KZ3 * sin(s(8)) * cos(s(7)) * sin(s(11)) * sin(s(10)) - JY3 * s(24) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - JY3 * s(23) * cos(s(12)) * sin(s(11)) * sin(s(10)) * sin(s(9)) * sin(s(7)) + KY3 * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(21) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + KY3 * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(21) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + JX1 * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) JX1 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JX1 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(6)) * cos(s(5)) * cos(s(4)) + JX1 * s(16) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(19) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(16) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + KY1 * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + KY1 * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JZ1 * s(16) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) + JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(6)) * cos(s(4)) + JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(21) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + JX1 * s(18) *

177 cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(21) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JZ1 * s(20) * sin(s(5)) * cos(s(4)) * cos(s(8)) * sin(s(7)) - JZ1 * s(19) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) - JZ1 * s(19) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) - JZ1 * s(17) * cos(s(5)) * cos(s(4)) * sin(s(8)) * sin(s(7)) - JX1 * s(19) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - KX1 * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - KY1 * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(6)) * sin(s(4)) - KX1 * cos(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(21) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + JY1 * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + JY1 * s(18) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + JX3 * s(23) * sin(s(12)) * sin(s(11)) * sin(s(10)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + JX3 * s(21) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(19) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(23) * sin(s(12)) * sin(s(11)) * sin(s(10)) * cos(s(9)) * sin(s(7)) + JX3 * s(23) * sin(s(12)) * sin(s(11)) * cos(s(10)) * cos(s(9)) * cos(s(7)) - JX3 * s(22) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(19) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(24) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - JX3 * s(24) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - KX3 * cos(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + KY3 * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(24) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JY3 * s(19) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JY3 * s(19) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - JY3 * s(23) * cos(s(12)) * sin(s(11)) * cos(s(10)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(22) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JY3 * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(19) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JY3 * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + JY3 * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(24) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JZ3 * s(23) * sin(s(8)) * sin(s(7)) * cos(s(11)) * cos(s(10)) - KY3 * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JY3 * s(21) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - JX3 * s(21) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + KX3 * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(19) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(24) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) JY3 * s(24) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JZ3 * s(22) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) - JZ3 * s(22) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) - JZ3 * s(20) * cos(s(8)) * cos(s(7)) * sin(s(11)) *

178 sin(s(10)) - JY3 * s(24) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(24) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JZ3 * s(23) * sin(s(8)) * cos(s(7)) * cos(s(11)) * sin(s(10)) - KX3 * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - KX3 * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(21) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JX3 * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - JY3 * s(21) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + KY3 * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + KX3 * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(21) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + KZ3 * sin(s(8)) * sin(s(7)) * sin(s(11)) * cos(s(10)) - JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(21) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(24) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(24) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + JY3 * s(21) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(18) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + JY1 * s(18) * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(18) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + JY1 * s(18) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JY1 * s(21) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(21) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - JY1 * s(21) * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JY1 * s(21) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + JY1 * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(19) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(6)) * sin(s(4)) - JY1 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(6)) * cos(s(4)) + KX1 * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - JY1 * s(21) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(16) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(16) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + JY1 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(6)) * cos(s(5)) * cos(s(4)) JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JY1 * s(18) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JY1 * s(16) * sin(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + JX1 * s(18) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + KY1 * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + JX1 * s(21) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + JY1 * s(18) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + JX1 * s(16) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - JX1 * s(21) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JX1 * s(18) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + KX1 * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + JZ1 * s(20) * sin(s(5)) * sin(s(4)) * cos(s(8)) * cos(s(7)) + JZ1 * s(17) * cos(s(5)) * sin(s(4)) * sin(s(8)) * cos(s(7)) + JZ1 * s(16) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) + KZ1 * sin(s(5)) * sin(s(4)) * sin(s(8)) * cos(s(7)) + JY1 * s(21) * sin(s(6)) * sin(s(4)) * cos(s(9))

179 * cos(s(7)) + KZ3 * d33 + JX3 * s(21) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + KX3 * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(21) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)); F8 = -cos(s(7)) * JX1 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(6)) * sin(s(4)) - KX3 * sin(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) cos(s(7)) * JZ1 * sin(s(5)) * sin(s(4)) * cos(s(8)) * s(16) - JY1 * s(21) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) + sin(s(7)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(8)) + cos(s(7)) * JY1 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(6)) * sin(s(4)) + cos(s(7)) * JY1 * cos(s(9)) * sin(s(8)) * s(16) * sin(s(6)) * cos(s(4)) - sin(s(7)) * JX1 * s(18) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * JX1 * s(18) * sin(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(4)) - JY1 * s(18) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) + sin(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * JX1 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * KZ3 * cos(s(8)) * sin(s(11)) * sin(s(10)) - cos(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * cos(s(10)) cos(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(10)) + sin(s(7)) * JY3 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(12)) * cos(s(10)) - cos(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(6)) * sin(s(4)) - JX1 * s(20) * sin(s(6)) * sin(s(5)) * sin(s(9)) * sin(s(8)) - sin(s(7)) * JZ3 * cos(s(8)) * sin(s(11)) * cos(s(10)) * s(22) - cos(s(7)) * KY3 * cos(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(10)) + sin(s(7)) * KZ1 * sin(s(5)) * sin(s(4)) * cos(s(8)) - sin(s(7)) * JX3 * s(23) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(11)) * sin(s(10)) - sin(s(7)) * JY3 * cos(s(9)) * sin(s(8)) * s(22) * sin(s(12)) * sin(s(10)) - sin(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * sin(s(10)) sin(s(7)) * JY3 * s(23) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(11)) * sin(s(10)) + sin(s(7)) * JY3 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + sin(s(7)) * JY3 * cos(s(9)) * sin(s(8)) * s(22) * cos(s(12)) * cos(s(11)) * cos(s(10)) cos(s(7)) * JY3 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(12)) * sin(s(10)) - cos(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(10)) - cos(s(7)) * JY1 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(6)) * cos(s(5)) * cos(s(4)) + sin(s(7)) * KZ3 * d32 + JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(11)) + KY1 * cos(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) + cos(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * KY3 * cos(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * JY3 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(10)) + sin(s(7)) * KY3 * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(10)) + sin(s(7)) * JZ3 * s(20) * sin(s(8)) * sin(s(11)) * sin(s(10)) + sin(s(7)) * KX3 * sin(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + sin(s(7)) * JX3 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + sin(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + sin(s(7)) * JX3 * sin(s(9)) * sin(s(8)) * s(22) * cos(s(12)) * sin(s(10)) + sin(s(7)) * JX3 * sin(s(9)) * sin(s(8)) * s(22) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(10)) + sin(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * JY1 *

180 cos(s(9)) * sin(s(8)) * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) sin(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - JY1 * s(20) * cos(s(6)) * sin(s(5)) * cos(s(9)) * sin(s(8)) - cos(s(7)) * JZ1 * s(20) * sin(s(5)) * cos(s(4)) * sin(s(8)) + sin(s(7)) * JX1 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(6)) * cos(s(4)) - cos(s(7)) * KZ3 * cos(s(8)) * sin(s(11)) * cos(s(10)) sin(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(10)) + JX1 * s(21) * sin(s(6)) * sin(s(5)) * cos(s(9)) * cos(s(8)) + JY3 * s(21) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) + sin(s(7)) * KY3 * cos(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JX1 * s(17) * sin(s(6)) * cos(s(5)) * sin(s(9)) * cos(s(8)) + sin(s(7)) * KX1 * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(4)) + sin(s(7)) * JZ1 * sin(s(5)) * cos(s(4)) * cos(s(8)) * s(16) + cos(s(7)) * KY1 * cos(s(9)) * sin(s(8)) * sin(s(6)) * sin(s(4)) + JY1 * s(17) * cos(s(6)) * cos(s(5)) * cos(s(9)) * cos(s(8)) + cos(s(7)) * JZ1 * s(17) * cos(s(5)) * cos(s(4)) * cos(s(8)) + JZ1 * s(17) * sin(s(5)) * sin(s(8)) - JZ1 * s(20) * cos(s(5)) * cos(s(8)) - JZ3 * s(23) * sin(s(8)) * sin(s(11)) - cos(s(7)) * KX1 * sin(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * cos(s(4)) + cos(s(7)) * JZ3 * cos(s(8)) * sin(s(11)) * sin(s(10)) * s(22) + cos(s(7)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(8)) + cos(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * cos(s(4)) - JX3 * sin(s(12)) * sin(s(11)) * s(19) * cos(s(9)) + cos(s(7)) * JX1 * sin(s(9)) * sin(s(8)) * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) + sin(s(7)) * JZ1 * s(17) * cos(s(5)) * sin(s(4)) * cos(s(8)) - cos(s(7)) * JX1 * sin(s(9)) * sin(s(8)) * s(16) * cos(s(6)) * cos(s(4)) - sin(s(7)) * JX3 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(12)) * cos(s(10)) + cos(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * cos(s(4)) + cos(s(7)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(8)) + cos(s(7)) * JY1 * cos(s(9)) * sin(s(8)) * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * JY1 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - cos(s(7)) * JX1 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(6)) * cos(s(5)) * cos(s(4)) + sin(s(7)) * JY1 * cos(s(9)) * sin(s(8)) * s(16) * sin(s(6)) * sin(s(4)) + sin(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(4)) - cos(s(7)) * JY3 * cos(s(9)) * sin(s(8)) * s(22) * sin(s(12)) * cos(s(10)) cos(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - cos(s(7)) * JY3 * s(23) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(11)) * cos(s(10)) - cos(s(7)) * JY3 * cos(s(9)) * sin(s(8)) * s(22) * cos(s(12)) * cos(s(11)) * sin(s(10)) JY1 * cos(s(6)) * sin(s(5)) * s(19) * sin(s(9)) + sin(s(7)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(8)) sin(s(7)) * JX1 * sin(s(9)) * sin(s(8)) * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) - KY3 * cos(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) sin(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(7)) * JX3 * s(23) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(11)) * cos(s(10)) - cos(s(7)) * JX3 * sin(s(9)) * sin(s(8)) * s(22) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JY3 * cos(s(12)) * sin(s(11)) * s(19) * sin(s(9)) - sin(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(10)) - cos(s(7)) * KX1 * sin(s(9)) * sin(s(8)) * cos(s(6)) * sin(s(4)) - sin(s(7)) * KX3 * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(10)) - sin(s(7)) * JZ3 * s(23) * cos(s(8)) * cos(s(11)) * sin(s(10)) - cos(s(7)) * JZ3 * s(23) * cos(s(8)) * cos(s(11)) * cos(s(10)) - cos(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(6)) * sin(s(4)) + cos(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(8)) * cos(s(6)) * sin(s(4)) + cos(s(7)) * JX1 *

181 s(18) * sin(s(9)) * sin(s(8)) * sin(s(6)) * sin(s(4)) + KX1 * sin(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) - sin(s(7)) * JX1 * sin(s(9)) * sin(s(8)) * s(16) * cos(s(6)) * sin(s(4)) - cos(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * cos(s(4)) - JX3 * s(23) * sin(s(12)) * cos(s(11)) * sin(s(9)) * cos(s(8)) + JX1 * sin(s(6)) * sin(s(5)) * s(19) * cos(s(9)) - JX3 * s(21) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) + sin(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(4)) + JZ3 * s(20) * cos(s(8)) * cos(s(11)) - JX3 * s(24) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) + cos(s(7)) * KZ1 * sin(s(5)) * cos(s(4)) * cos(s(8)) - sin(s(7)) * KY1 * cos(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(4)) - sin(s(7)) * JZ1 * s(20) * sin(s(5)) * sin(s(4)) * sin(s(8)) - cos(s(7)) * KY1 * cos(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * cos(s(4)) - sin(s(7)) * JY1 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(6)) * cos(s(4)) - sin(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(4)) + sin(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(10)) - cos(s(7)) * JX1 * s(18) * sin(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * cos(s(4)) sin(s(7)) * KY1 * cos(s(9)) * sin(s(8)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - JY3 * s(23) * cos(s(12)) * cos(s(11)) * cos(s(9)) * cos(s(8)) - sin(s(7)) * KX1 * sin(s(9)) * sin(s(8)) * sin(s(6)) * cos(s(5)) * sin(s(4)) + cos(s(7)) * KZ1 * d11 + cos(s(7)) * KZ3 * d31 + KZ3 * sin(s(8)) * cos(s(11)) + sin(s(7)) * KZ1 * d12 - KZ1 * cos(s(5)) * sin(s(8)) + sin(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(7)) * KX3 * sin(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(10)) + cos(s(7)) * JX3 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(12)) * sin(s(10)) + cos(s(7)) * JX3 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(10)) + cos(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * JX3 * sin(s(9)) * sin(s(8)) * s(22) * cos(s(12)) * cos(s(10)) + JX1 * s(18) * cos(s(6)) * sin(s(5)) * sin(s(9)) * cos(s(8)) + JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(11)) + cos(s(7)) * KX3 * sin(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(24) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) + cos(s(7)) * JZ3 * s(20) * sin(s(8)) * sin(s(11)) * cos(s(10)); F9 = -cos(s(8)) ^ 2 * JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(8)) * KY1 * sin(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(8)) * KY1 * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(7)) * KY1 * cos(s(9)) * cos(s(6)) * cos(s(5)) * sin(s(4)) + cos(s(7)) * JZ1 * s(20) * sin(s(5)) * sin(s(4)) + cos(s(7)) * JY1 * s(18) * cos(s(9)) * cos(s(6)) * cos(s(4)) + sin(s(8)) * JY3 * s(21) * cos(s(12)) * sin(s(11)) * cos(s(9)) + sin(s(7)) * KX3 * sin(s(9)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * JX3 * s(19) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + sin(s(7)) * KY3 * cos(s(9)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) ^ 2 * JX3 * s(19) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(8)) ^ 2 * JX3 * s(19) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(8)) * JX1 * s(17) * sin(s(6)) * cos(s(5)) * cos(s(9)) + cos(s(8)) * JX3 * s(19) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(8)) ^ 2 * JX3 * s(19) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(8)) * JX3 * s(19) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(8)) * JX1 * s(18) * cos(s(6)) * sin(s(5)) * cos(s(9)) + cos(s(7)) * JY3 * cos(s(9)) * s(22) * sin(s(12)) * sin(s(10)) - cos(s(8)) * JX3 * s(24) * cos(s(9))

182 * sin(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(7)) * JX3 * sin(s(9)) * s(22) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(7)) * JY1 * s(18) * cos(s(9)) * cos(s(6)) * sin(s(4)) - cos(s(8)) * JY3 * s(24) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(7)) * JX3 * s(21) * cos(s(9)) * cos(s(12)) * sin(s(10)) + sin(s(7)) * JY1 * cos(s(9)) * s(16) * sin(s(6)) * cos(s(4)) - cos(s(8)) * JX3 * s(24) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - sin(s(7)) * JX1 * s(21) * cos(s(9)) * cos(s(6)) * sin(s(4)) - sin(s(8)) * JY1 * s(21) * cos(s(6)) * sin(s(5)) * cos(s(9)) - sin(s(7)) * KY1 * cos(s(9)) * cos(s(6)) * cos(s(5)) * cos(s(4)) cos(s(7)) * KY3 * cos(s(9)) * cos(s(12)) * cos(s(11)) * sin(s(10)) cos(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(6)) * cos(s(4)) + sin(s(8)) * JX3 * sin(s(12)) * sin(s(11)) * s(19) * sin(s(9)) * cos(s(8)) + cos(s(8)) * JY3 * s(19) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(8)) * JY3 * s(19) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(8)) * JY3 * s(24) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + sin(s(8)) * JY1 * s(18) * sin(s(6)) * sin(s(5)) * sin(s(9)) - sin(s(8)) * cos(s(7)) * KZ3 * d32 JZ1 * cos(s(5)) * s(19) * cos(s(8)) ^ 2 + sin(s(8)) * sin(s(7)) * KZ1 * d11 + sin(s(8)) * sin(s(7)) * KZ3 * d31 + JZ3 * cos(s(11)) * s(19) * cos(s(8)) ^ 2 + cos(s(8)) * JX1 * s(18) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(8)) ^ 2 * JY3 * s(19) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - sin(s(7)) * KY3 * cos(s(9)) * sin(s(12)) * sin(s(10)) - cos(s(8)) * JZ1 * s(19) * sin(s(5)) * cos(s(4)) * sin(s(8)) * cos(s(7)) - cos(s(7)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) - sin(s(8)) * JX3 * s(24) * cos(s(12)) * sin(s(11)) * cos(s(9)) - cos(s(7)) * KX3 * sin(s(9)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * JZ1 * s(19) * sin(s(5)) * sin(s(4)) * sin(s(8)) * sin(s(7)) - sin(s(7)) * JY3 * cos(s(9)) * s(22) * sin(s(12)) * cos(s(10)) - sin(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(12)) * sin(s(10)) + sin(s(7)) * JY1 * cos(s(9)) * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) - cos(s(7)) * JY1 * cos(s(9)) * s(16) * sin(s(6)) * sin(s(4)) + sin(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(6)) * cos(s(5)) * cos(s(4)) - cos(s(7)) * JX3 * sin(s(9)) * s(22) * cos(s(12)) * sin(s(10)) - sin(s(7)) * JY1 * s(21) * sin(s(9)) * sin(s(6)) * sin(s(4)) + sin(s(8)) * KX1 * sin(s(6)) * sin(s(5)) * cos(s(9)) + sin(s(7)) * JX1 * sin(s(9)) * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) + cos(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - sin(s(7)) * JY3 * cos(s(9)) * s(22) * cos(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * JX1 * s(21) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * JY3 * s(22) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * JY3 * s(21) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(7)) * JY3 * cos(s(9)) * s(22) * cos(s(12)) * cos(s(11)) * cos(s(10)) - cos(s(8)) * JX3 * s(22) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - cos(s(8)) * JX3 * s(19) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) cos(s(8)) * KY1 * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - cos(s(8)) * JX3 * s(24) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - sin(s(8)) * JX1 * s(21) * sin(s(6)) * sin(s(5)) * sin(s(9)) - cos(s(7)) * JY1 * s(18) * cos(s(9)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(8)) * JY3 * s(24) * sin(s(12)) * sin(s(11)) * sin(s(9)) + cos(s(7)) * KX3 * sin(s(9)) * cos(s(12)) * cos(s(10)) + cos(s(7)) * JX1 * s(18) * sin(s(9)) * sin(s(6)) * cos(s(4)) - cos(s(8)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(8)) * JY1 * s(21) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(7)) *

183 JX3 * s(23) * sin(s(9)) * sin(s(12)) * sin(s(11)) * sin(s(10)) + cos(s(7)) * JY1 * cos(s(9)) * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) - cos(s(8)) * JY3 * s(23) * cos(s(12)) * sin(s(11)) * sin(s(10)) * sin(s(9)) * sin(s(7)) + cos(s(8)) * KY1 * sin(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * KX1 * cos(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + sin(s(7)) * JZ3 * s(20) * sin(s(11)) * cos(s(10)) + sin(s(8)) * JY3 * cos(s(12)) * sin(s(11)) * s(19) * cos(s(9)) * cos(s(8)) - cos(s(8)) * JY1 * s(16) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(8)) * JY3 * s(22) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) cos(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * JY1 * s(18) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(8)) * JY1 * s(19) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - cos(s(8)) ^ 2 * JY1 * s(19) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(7)) * JX1 * sin(s(9)) * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) + sin(s(7)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) - cos(s(8)) * JY1 * s(19) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * JX3 * s(23) * sin(s(12)) * sin(s(11)) * sin(s(10)) * cos(s(9)) * sin(s(7)) + cos(s(8)) * JX3 * s(23) * sin(s(12)) * sin(s(11)) * cos(s(10)) * cos(s(9)) * cos(s(7)) + cos(s(8)) * JX3 * s(22) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(8)) * JX3 * s(21) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * JY1 * s(19) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(8)) ^ 2 * JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(8)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * JY1 * s(17) * cos(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - sin(s(8)) * cos(s(7)) * KZ1 * d12 + cos(s(8)) * JY1 * s(16) * cos(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + sin(s(7)) * JY1 * s(21) * sin(s(9)) * cos(s(6)) * cos(s(5)) * cos(s(4)) - cos(s(8)) * JY1 * s(21) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(8)) * JY1 * s(19) * cos(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(8)) * JY1 * s(18) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * JY1 * s(18) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) cos(s(8)) * JY1 * s(21) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(8)) * JY3 * s(22) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - sin(s(7)) * KX1 * sin(s(9)) * sin(s(6)) * cos(s(5)) * cos(s(4)) - sin(s(7)) * JX1 * sin(s(9)) * s(16) * cos(s(6)) * cos(s(4)) - cos(s(8)) * JX1 * s(16) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(8)) * JY3 * s(23) * cos(s(12)) * sin(s(11)) * cos(s(10)) * sin(s(9)) * cos(s(7)) cos(s(8)) * JY3 * s(22) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(8)) * JX1 * s(19) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) - sin(s(7)) * JY3 * s(21) * sin(s(9)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - sin(s(8)) * JX1 * sin(s(6)) * sin(s(5)) * s(19) * sin(s(9)) * cos(s(8)) - cos(s(7)) * KX1 * sin(s(9)) * cos(s(6)) * cos(s(4)) - sin(s(7)) * JX3 * sin(s(9)) * s(22) * sin(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(7)) * JX3 * s(24) * sin(s(9)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - sin(s(7)) * JX1 * s(18) * sin(s(9)) * cos(s(6)) * cos(s(5)) * cos(s(4)) - sin(s(7)) * JX3 * s(23) * sin(s(9)) * sin(s(12)) * sin(s(11)) * cos(s(10)) - sin(s(8)) * JY1 * cos(s(6)) * sin(s(5)) * s(19) * cos(s(9)) * cos(s(8)) cos(s(8)) * KX3 * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(8)) * JX1 * s(18) * cos(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(8)) * JX3 * s(21) * sin(s(9))

184 * sin(s(7)) * cos(s(12)) * cos(s(10)) - sin(s(7)) * JZ1 * s(20) * sin(s(5)) * cos(s(4)) - sin(s(7)) * JY3 * s(23) * cos(s(9)) * cos(s(12)) * sin(s(11)) * cos(s(10)) - cos(s(7)) * JZ3 * s(20) * sin(s(11)) * sin(s(10)) + cos(s(8)) * JX1 * s(16) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(7)) * KY3 * cos(s(9)) * sin(s(12)) * cos(s(10)) - cos(s(8)) * JX3 * s(22) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - sin(s(8)) * JX3 * s(23) * cos(s(9)) * sin(s(12)) * cos(s(11)) - cos(s(8)) * KY3 * sin(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(8)) * KX3 * cos(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - sin(s(7)) * JY3 * s(24) * cos(s(9)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + sin(s(7)) * KX3 * sin(s(9)) * cos(s(12)) * sin(s(10)) - sin(s(7)) * JY3 * s(24) * cos(s(9)) * cos(s(12)) * sin(s(10)) - cos(s(8)) ^ 2 * JX3 * s(19) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - cos(s(7)) * JX1 * s(21) * cos(s(9)) * cos(s(6)) * cos(s(4)) - cos(s(8)) * JX1 * s(21) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - sin(s(8)) * JY1 * s(17) * cos(s(6)) * cos(s(5)) * sin(s(9)) - cos(s(8)) * JX3 * s(22) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) ^ 2 * JY1 * s(19) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(8)) ^ 2 * JY3 * s(19) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * KX3 * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * JY3 * s(19) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(8)) ^ 2 * JY3 * s(19) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(7)) * JX1 * s(18) * sin(s(9)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - sin(s(7)) * KX1 * sin(s(9)) * cos(s(6)) * sin(s(4)) + cos(s(8)) * JY3 * s(21) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - cos(s(8)) * KX1 * cos(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) - cos(s(7)) * JY3 * s(24) * cos(s(9)) * cos(s(12)) * cos(s(10)) - cos(s(8)) ^ 2 * JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * sin(s(9)) * cos(s(7)) + cos(s(8)) * KX1 * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(8)) * KX1 * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(8)) * JX1 * s(18) * sin(s(6)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(8)) * JX1 * s(16) * cos(s(6)) * cos(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(8)) * JY1 * s(16) * sin(s(6)) * cos(s(4)) * sin(s(9)) * cos(s(7)) - cos(s(8)) * JX1 * s(21) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(8)) * JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - cos(s(7)) * JX3 * s(24) * sin(s(9)) * sin(s(12)) * cos(s(10)) - cos(s(8)) * JX1 * s(18) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) - sin(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(6)) * cos(s(5)) * cos(s(4)) - cos(s(8)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * cos(s(9)) * cos(s(7)) cos(s(8)) ^ 2 * JX1 * s(19) * sin(s(6)) * cos(s(5)) * sin(s(4)) * sin(s(9)) * sin(s(7)) - cos(s(8)) ^ 2 * JX1 * s(19) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) - cos(s(8)) * JX1 * s(19) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) - sin(s(8)) * KY1 * cos(s(6)) * sin(s(5)) * sin(s(9)) - cos(s(7)) * JY1 * s(21) * sin(s(9)) * cos(s(6)) * cos(s(5)) * sin(s(4)) - cos(s(8)) * JX1 * s(19) * sin(s(6)) * cos(s(5)) * cos(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(7)) * JX3 * s(21) * cos(s(9)) * cos(s(12)) * cos(s(10)) + cos(s(8)) * JY1 * s(16) * sin(s(6)) * sin(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(8)) * JY1 * s(18) * cos(s(6)) * sin(s(4)) * sin(s(9)) * cos(s(7)) + sin(s(7)) * JX3 * s(24) * sin(s(9)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * JX1 * s(16) * cos(s(6)) * sin(s(4)) * cos(s(9)) * sin(s(7)) + cos(s(7)) * JY3 * s(21) * sin(s(9)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + sin(s(7)) * JX3 * s(21) * cos(s(9)) * sin(s(12)) * cos(s(11)) *

185 cos(s(10)) + cos(s(7)) * KY1 * cos(s(9)) * sin(s(6)) * cos(s(4)) + cos(s(7)) * JX1 * s(21) * cos(s(9)) * sin(s(6)) * cos(s(5)) * sin(s(4)) + cos(s(7)) * JY3 * s(23) * cos(s(9)) * cos(s(12)) * sin(s(11)) * sin(s(10)) - JZ3 * cos(s(11)) * s(19) + cos(s(8)) * KZ1 * d13 + JZ1 * cos(s(5)) * s(19) + cos(s(8)) * KZ3 * d33 - cos(s(7)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * sin(s(4)) * sin(s(9)) + sin(s(8)) * KY3 * cos(s(12)) * sin(s(11)) * sin(s(9)) + sin(s(7)) * KY1 * cos(s(9)) * sin(s(6)) * sin(s(4)) + sin(s(7)) * JX1 * s(17) * sin(s(6)) * sin(s(5)) * cos(s(4)) * sin(s(9)) + cos(s(7)) * JX1 * sin(s(9)) * s(16) * cos(s(6)) * sin(s(4)) + cos(s(8)) * JX1 * s(21) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(8)) ^ 2 * JX1 * s(19) * cos(s(6)) * cos(s(4)) * sin(s(9)) * sin(s(7)) + cos(s(8)) * JZ3 * s(19) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) + cos(s(8)) * KX3 * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(8)) * JX3 * s(21) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(8)) * JX3 * s(21) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * KY3 * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * KY3 * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(8)) * KY3 * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + cos(s(8)) * JY3 * s(21) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(8)) * JX3 * s(24) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(8)) * JY1 * s(21) * sin(s(6)) * sin(s(4)) * cos(s(9)) * cos(s(7)) + cos(s(8)) * JZ3 * s(19) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) + sin(s(8)) * JX3 * s(21) * sin(s(12)) * sin(s(11)) * sin(s(9)) + sin(s(7)) * JX1 * s(18) * sin(s(9)) * sin(s(6)) * sin(s(4)) + cos(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(12)) * cos(s(10)) + sin(s(7)) * JY3 * s(21) * sin(s(9)) * sin(s(12)) * sin(s(10)) + sin(s(8)) * JY3 * s(23) * sin(s(9)) * cos(s(12)) * cos(s(11)) + cos(s(7)) * KX1 * sin(s(9)) * sin(s(6)) * cos(s(5)) * sin(s(4)) - cos(s(8)) * JY3 * s(21) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + sin(s(7)) * JX3 * sin(s(9)) * s(22) * cos(s(12)) * cos(s(10)) - sin(s(8)) * KX3 * sin(s(12)) * sin(s(11)) * cos(s(9)) - cos(s(8)) * JY3 * s(24) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - cos(s(8)) * JY3 * s(19) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + cos(s(8)) * JY3 * s(24) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(8)) ^ 2 * JY3 * s(19) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)); F10 = -JZ3 * s(20) * cos(s(8)) * sin(s(7)) * sin(s(11)) * cos(s(10)) + JX3 * s(23) * sin(s(12)) * sin(s(11)) * cos(s(10)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - JZ3 * s(19) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) - JZ3 * s(19) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) + JY3 * s(22) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + KY3 * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - KX3 * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - JX3 * s(19) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - JY3 * s(24) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(22) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(19) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(24) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(24) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - JY3 * s(23) * cos(s(12)) * sin(s(11)) * sin(s(10)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - JX3 * s(21) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - JY3 * s(21) * cos(s(9)) *

186 cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - JX3 * s(22) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(21) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(23) * cos(s(12)) * sin(s(11)) * cos(s(10)) * sin(s(9)) * cos(s(7)) + JY3 * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + JY3 * s(24) * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(22) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + JX3 * s(22) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(22) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - JX3 * s(24) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - JX3 * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JY3 * s(21) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + KX3 * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + KY3 * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + KY3 * sin(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + KZ3 * sin(s(8)) * cos(s(7)) * sin(s(11)) * sin(s(10)) + JY3 * s(24) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(23) * cos(s(12)) * sin(s(11)) * sin(s(10)) * sin(s(9)) * sin(s(7)) - KY3 * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(21) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - KY3 * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(21) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - JX3 * s(23) * sin(s(12)) * sin(s(11)) * sin(s(10)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - JX3 * s(21) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(19) * cos(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(23) * sin(s(12)) * sin(s(11)) * sin(s(10)) * cos(s(9)) * sin(s(7)) - JX3 * s(23) * sin(s(12)) * sin(s(11)) * cos(s(10)) * cos(s(9)) * cos(s(7)) + JX3 * s(22) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(19) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(24) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + JX3 * s(24) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + KX3 * cos(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - KY3 * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(24) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JY3 * s(19) * sin(s(9)) *

187 sin(s(7)) * sin(s(12)) * sin(s(10)) - JY3 * s(19) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + JY3 * s(23) * cos(s(12)) * sin(s(11)) * cos(s(10)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(22) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - JY3 * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JY3 * s(19) * sin(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - JY3 * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - JY3 * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(24) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - JZ3 * s(23) * sin(s(8)) * sin(s(7)) * cos(s(11)) * cos(s(10)) + KY3 * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - JY3 * s(21) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + JX3 * s(21) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - KX3 * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(19) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) + JY3 * s(24) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(24) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JZ3 * s(22) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) + JZ3 * s(22) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) + JZ3 * s(20) * cos(s(8)) * cos(s(7)) * sin(s(11)) * sin(s(10)) + JY3 * s(24) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + JY3 * s(24) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JZ3 * s(23) * sin(s(8)) * cos(s(7)) * cos(s(11)) * sin(s(10)) + KX3 * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) + KX3 * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) * sin(s(10)) - JX3 * s(21) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) JX3 * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + JY3 * s(21) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - KY3 * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - KX3 * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(21) * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) - KZ3 * sin(s(8)) * sin(s(7)) * sin(s(11)) * cos(s(10)) + JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(11)) * cos(s(10)) - JX3 * s(21) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(11)) * cos(s(10)) + JX3 * s(24) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) * sin(s(10)) + JX3 * s(24) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - JY3 * s(21) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - KZ3 * d33 - JX3 * s(21) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - KX3 * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - JY3 * s(21) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)); F11 = JY3 * cos(s(9)) * sin(s(8)) * s(22) * sin(s(12)) - JZ3 * s(20) * sin(s(8)) * sin(s(11)) + JZ3 * s(23) * cos(s(8)) * cos(s(11)) + cos(s(10)) * JZ3 * s(23) * sin(s(8)) * cos(s(7)) * sin(s(11)) - JX3 * sin(s(9)) * sin(s(8)) * s(22) * cos(s(12)) + sin(s(10)) * JY3 * s(23) * cos(s(12)) * cos(s(11)) * cos(s(9)) * cos(s(8)) * sin(s(7)) cos(s(10)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(11)) - cos(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(11)) * cos(s(9)) * sin(s(7)) - KY3 * cos(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) - cos(s(10)) * KZ3 * sin(s(8)) * cos(s(7)) * cos(s(11)) - cos(s(10)) * KY3 * cos(s(12)) * sin(s(11)) * sin(s(9)) *

188 sin(s(7)) + cos(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * JY3 * s(23) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(11)) + JX3 * s(23) * sin(s(9)) * sin(s(8)) * sin(s(12)) * sin(s(11)) + sin(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(10)) * JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(11)) + sin(s(10)) * JX3 * s(23) * sin(s(12)) * cos(s(11)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(10)) * KY3 * cos(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(11)) * cos(s(9)) * sin(s(7)) - KX3 * sin(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) + sin(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(10)) * JY3 * cos(s(12)) * sin(s(11)) * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * JX3 * s(23) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(11)) sin(s(10)) * KZ3 * sin(s(8)) * sin(s(7)) * cos(s(11)) - sin(s(10)) * JZ3 * sin(s(8)) * cos(s(7)) * cos(s(11)) * s(19) - sin(s(10)) * JZ3 * s(20) * cos(s(8)) * sin(s(7)) * cos(s(11)) - sin(s(10)) * KX3 * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(7)) + cos(s(10)) * JZ3 * sin(s(8)) * sin(s(7)) * cos(s(11)) * s(19) + JY3 * s(24) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) + JY3 * s(23) * cos(s(9)) * sin(s(8)) * cos(s(12)) * sin(s(11)) + JY3 * s(21) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) + cos(s(10)) * KX3 * sin(s(12)) * sin(s(11)) * cos(s(9)) * sin(s(7)) - cos(s(10)) * KZ3 * d31 sin(s(10)) * KZ3 * d32 + KZ3 * cos(s(8)) * sin(s(11)) + sin(s(10)) * KX3 * sin(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(10)) * JX3 * sin(s(12)) * sin(s(11)) * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(10)) * JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(11)) cos(s(10)) * JY3 * cos(s(12)) * sin(s(11)) * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(10)) * JZ3 * s(23) * sin(s(8)) * sin(s(7)) * sin(s(11)) + sin(s(10)) * KY3 * cos(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(7)) + sin(s(10)) * KY3 * cos(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(10)) * JY3 * s(23) * cos(s(12)) * cos(s(11)) * sin(s(9)) * cos(s(7)) - JX3 * s(21) * cos(s(9)) * sin(s(8)) * sin(s(12)) * cos(s(11)) - JX3 * s(20) * sin(s(9)) * cos(s(8)) * sin(s(12)) * cos(s(11)) - cos(s(10)) * JY3 * s(23) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(11)) + cos(s(10)) * JX3 * s(23) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(11)) + cos(s(10)) * JX3 * sin(s(12)) * sin(s(11)) * s(19) * cos(s(9)) * cos(s(7)) + cos(s(10)) * KX3 * sin(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(11)) * sin(s(9)) * sin(s(7)) - JY3 * s(20) * cos(s(9)) * cos(s(8)) * cos(s(12)) * cos(s(11)) + sin(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(7)) - cos(s(10)) * JZ3 * s(20) * cos(s(8)) * cos(s(7)) * cos(s(11)) - cos(s(10)) * JY3 * cos(s(12)) * sin(s(11)) * s(19) * sin(s(9)) * cos(s(7)) - JX3 * s(24) * sin(s(9)) * sin(s(8)) * cos(s(12)) * cos(s(11)) + sin(s(10)) * JX3 * sin(s(12)) * sin(s(11)) * s(19) * cos(s(9)) * sin(s(7)) + sin(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(7)) sin(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(11)) * sin(s(9)) * cos(s(7)) - sin(s(10)) * JY3 * cos(s(12)) *

189 sin(s(11)) * s(19) * sin(s(9)) * sin(s(7)) - sin(s(10)) * JX3 * s(23) * sin(s(12)) * cos(s(11)) * cos(s(9)) * cos(s(7)) - sin(s(10)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(11)) sin(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(7)) - cos(s(10)) * JX3 * sin(s(12)) * sin(s(11)) * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(11)) * cos(s(9)) * cos(s(8)) * cos(s(7)) cos(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(11)) * sin(s(9)) * sin(s(7)); F12 = sin(s(11)) * JX3 * sin(s(9)) * sin(s(8)) * s(22) * sin(s(12)) * cos(s(11)) + sin(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(11)) * KX3 * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) - sin(s(10)) * JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) - cos(s(10)) * JX3 * sin(s(12)) * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) - sin(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(9)) * sin(s(7)) - cos(s(11)) * JY3 * s(24) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + sin(s(11)) * KY3 * cos(s(9)) * sin(s(8)) * sin(s(12)) - sin(s(10)) * JY3 * cos(s(12)) * s(19) * sin(s(9)) * cos(s(7)) + cos(s(11)) ^ 2 * JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(11)) ^ 2 * JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - cos(s(11)) * KX3 * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - cos(s(11)) ^ 2 * JX3 * s(22) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(11)) * JX3 * s(24) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(24) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(10)) * JY3 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) + cos(s(11)) * KY3 * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + sin(s(11)) * JY3 * cos(s(9)) * sin(s(8)) * s(22) * cos(s(12)) * cos(s(11)) - cos(s(10)) * JX3 * sin(s(12)) * s(19) * cos(s(9)) * sin(s(7)) - sin(s(10)) * JX3 * sin(s(12)) * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(11)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(11)) * JX3 * s(19) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) sin(s(10)) * JY3 * s(24) * sin(s(12)) * cos(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(11)) ^ 2 * JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(11)) * JX3 * s(22) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) ^ 2 * JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - sin(s(10)) * JY3 * cos(s(12)) * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(11)) * JX3 * s(21) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) cos(s(10)) * KY3 * cos(s(12)) * sin(s(9)) * cos(s(7)) - sin(s(11)) * sin(s(10)) * KZ3 * d31 + JZ3 * cos(s(8)) * s(22) * cos(s(11)) ^ 2 + sin(s(11)) * cos(s(10)) * KZ3 * d32 - cos(s(11)) ^ 2 * JY3 * s(22) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - cos(s(10)) * JZ3 * s(23) * sin(s(8)) * sin(s(7)) + sin(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(9)) * sin(s(7)) + cos(s(10)) * JY3 * s(24) * sin(s(12)) * sin(s(9)) * cos(s(7)) + sin(s(11)) * JY3 * s(20) * cos(s(9)) * cos(s(8)) * sin(s(12)) + cos(s(11)) * JY3 * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) - sin(s(11)) * JX3 * s(21) * cos(s(9)) * sin(s(8)) * cos(s(12)) + cos(s(11)) * JY3 * s(22) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(11)) * JY3 * s(19) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(11)) *

190 JX3 * s(22) * sin(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * cos(s(10)) - cos(s(11)) * JX3 * s(21) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - cos(s(11)) * JY3 * s(21) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + sin(s(10)) * JZ3 * s(23) * sin(s(8)) * cos(s(7)) - cos(s(10)) * KX3 * sin(s(12)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + cos(s(11)) * JY3 * s(22) * sin(s(9)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(11)) * KY3 * sin(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(10)) * JX3 * s(21) * sin(s(12)) * sin(s(9)) * cos(s(7)) - cos(s(10)) * KY3 * cos(s(12)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(10)) * JY3 * s(21) * cos(s(12)) * cos(s(9)) * sin(s(7)) - sin(s(11)) * JY3 * s(21) * sin(s(9)) * sin(s(8)) * sin(s(12)) - cos(s(10)) * JX3 * s(21) * sin(s(12)) * cos(s(9)) * cos(s(8)) * sin(s(7)) - sin(s(10)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) - sin(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(11)) * JY3 * s(22) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(10)) * JX3 * s(24) * cos(s(12)) * sin(s(9)) * cos(s(8)) * sin(s(7)) - cos(s(11)) * JY3 * s(19) * sin(s(9)) * sin(s(7)) * sin(s(12)) * sin(s(10)) - cos(s(11)) * JY3 * s(21) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) - cos(s(10)) * JY3 * s(21) * cos(s(12)) * cos(s(9)) * cos(s(7)) - cos(s(11)) * JX3 * s(19) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(11)) ^ 2 * JX3 * s(22) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(11)) * JX3 * s(22) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) - cos(s(11)) * KZ3 * d33 - JZ3 * cos(s(8)) * s(22) + cos(s(11)) * JY3 * s(24) * cos(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(11)) * JY3 * s(24) * cos(s(9)) * cos(s(8)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) ^ 2 * JY3 * s(22) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - sin(s(10)) * KY3 * cos(s(12)) * sin(s(9)) * sin(s(7)) + cos(s(11)) * JY3 * s(21) * cos(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(10)) * JY3 * s(24) * sin(s(12)) * cos(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(11)) * JY3 * s(24) * cos(s(9)) * sin(s(8)) * cos(s(12)) - cos(s(11)) * JY3 * s(20) * cos(s(9)) * sin(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) + sin(s(10)) * JX3 * sin(s(12)) * s(19) * cos(s(9)) * cos(s(7)) cos(s(11)) * JY3 * s(22) * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + sin(s(11)) * JX3 * s(24) * sin(s(9)) * sin(s(8)) * sin(s(12)) + sin(s(10)) * JX3 * s(21) * sin(s(12)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(11)) * JX3 * s(21) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(22) * cos(s(9)) * cos(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(10)) * JX3 * s(20) * sin(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) + sin(s(10)) * KX3 * sin(s(12)) * cos(s(9)) * sin(s(7)) - cos(s(10)) * JY3 * cos(s(12)) * s(19) * cos(s(9)) * cos(s(8)) * cos(s(7)) cos(s(11)) * JY3 * s(21) * sin(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(24) * sin(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) - sin(s(11)) * JX3 * s(20) * sin(s(9)) * cos(s(8)) * cos(s(12)) + cos(s(11)) * KY3 * cos(s(9)) * cos(s(8)) * cos(s(7)) * sin(s(12)) * cos(s(10)) cos(s(11)) * JX3 * s(19) * cos(s(9)) * sin(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) * JY3 * s(24) * sin(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(21) * sin(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + cos(s(11)) * JZ3 * s(22) * sin(s(8)) * cos(s(7)) * sin(s(11)) * cos(s(10)) + cos(s(11)) * JZ3 * s(22) * sin(s(8)) * sin(s(7)) * sin(s(11)) * sin(s(10)) - cos(s(11)) * KX3 * cos(s(9)) * sin(s(7)) * cos(s(12)) * cos(s(10)) + sin(s(10)) * KY3 * cos(s(12)) * cos(s(9)) * cos(s(8)) * cos(s(7)) - cos(s(11)) * JY3

191 * s(20) * cos(s(9)) * sin(s(8)) * sin(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(10)) * JX3 * s(24) * cos(s(12)) * cos(s(9)) * cos(s(7)) cos(s(11)) * JY3 * s(19) * cos(s(9)) * cos(s(8)) * sin(s(7)) * sin(s(12)) * cos(s(10)) + cos(s(10)) * JY3 * cos(s(12)) * s(19) * sin(s(9)) * sin(s(7)) + cos(s(11)) * KX3 * cos(s(9)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - cos(s(11)) * JX3 * s(19) * sin(s(9)) * cos(s(8)) * cos(s(7)) * cos(s(12)) * sin(s(10)) - sin(s(11)) * KX3 * sin(s(9)) * sin(s(8)) * cos(s(12)) + cos(s(10)) * JY3 * s(21) * cos(s(12)) * sin(s(9)) * cos(s(8)) * sin(s(7)) + sin(s(10)) * JX3 * s(24) * cos(s(12)) * cos(s(9)) * sin(s(7)) + sin(s(10)) * KX3 * sin(s(12)) * sin(s(9)) * cos(s(8)) * cos(s(7)) + cos(s(10)) * KX3 * sin(s(12)) * cos(s(9)) * cos(s(7)) + cos(s(11)) * KY3 * sin(s(9)) * cos(s(7)) * sin(s(12)) * sin(s(10)) + cos(s(11)) * JX3 * s(24) * cos(s(9)) * sin(s(7)) * sin(s(12)) * cos(s(10));

Coefficient Constants in ‘for loop’ Form – Csi.m %The coefficent constants are listed in this script file reformatted be calculated in a 'for loop'. %This also includes generalized forces

F1-F12

%EQ 1 C1 = m1 * l1 * sin(s(i,5)) * cos(s(i,4)) / (m1 + m2 + m3) / 0.2e1; C2 = m1 * l1 * cos(s(i,5)) * sin(s(i,4)) / (m1 + m2 + m3) / 0.2e1; C3 = (m1 * l2 * sin(s(i,8)) * cos(s(i,7)) - m3 * l2 * sin(s(i,8)) * cos(s(i,7))) / (m1 + m2 + m3) / 0.2e1; C4 = (-m3 * l2 * cos(s(i,8)) * sin(s(i,7)) + m1 * l2 * cos(s(i,8)) * sin(s(i,7))) / (m1 + m2 + m3) / 0.2e1; C5 = -m3 * l3 * sin(s(i,11)) * cos(s(i,10)) / (m1 + m2 + m3) / 0.2e1; C6 = -m3 * l3 * cos(s(i,11)) * sin(s(i,10)) / (m1 + m2 + m3) / 0.2e1; C7 = (0.2e1 * m1 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) m1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m3 * l3 * cos(s(i,11)) * s(i,23) * cos(s(i,10)) * s(i,22) - m1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - m1 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) + 0.2e1 * m1 * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) - m1 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 + (2 * F1) + m3 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + m3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - 0.2e1 * m3 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) + m3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + m3 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10))) / (m1 + m2 + m3) / 0.2e1; %EQ 2 C8 = m1 * l1 * sin(s(i,5)) * sin(s(i,4)) / (m1 + m2 + m3) / 0.2e1; C9 = -m1 * l1 * cos(s(i,5)) * cos(s(i,4)) / (m1 + m2 + m3) / 0.2e1; C10 = (m1 * l2 * sin(s(i,8)) * sin(s(i,7)) - m3 * l2 * sin(s(i,8)) * sin(s(i,7))) / (m1 + m2 + m3) / 0.2e1; C11 = (m3 * l2 * cos(s(i,8)) * cos(s(i,7)) - m1 * l2 * cos(s(i,8)) * cos(s(i,7))) / (m1 + m2 + m3) / 0.2e1; C12 = -m3 * l3 * sin(s(i,11)) * sin(s(i,10)) / (m1 + m2 + m3) / 0.2e1; C13 = m3 * l3 * cos(s(i,11)) * cos(s(i,10)) / (m1 + m2 + m3) / 0.2e1; C14 = (0.2e1 * m1 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) + m1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m3 * l3 *

192 cos(s(i,11)) * s(i,23) * sin(s(i,10)) * s(i,22) + m1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + m1 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) + 0.2e1 * m1 * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) + m1 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 + (2 * F2) - m3 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 - m3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - 0.2e1 * m3 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - m3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - m3 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10))) / (m1 + m2 + m3) / 0.2e1; %EQ 3 C15 = -m1 * sin(s(i,5)) * l1 / (m1 + m2 + m3) / 0.2e1; C16 = -(m1 * sin(s(i,8)) * l2 - m3 * sin(s(i,8)) * l2) / (m1 + m2 + m3) / 0.2e1; C17 = m3 * sin(s(i,11)) * l3 / (m1 + m2 + m3) / 0.2e1; C18 = -(m1 * cos(s(i,8)) * s(i,20) ^ 2 * l2 + (2 * m2 * g) + m1 * cos(s(i,5)) * s(i,17) ^ 2 * l1 + 0.2e1 * m1 * g - m3 * cos(s(i,8)) * s(i,20) ^ 2 * l2 - m3 * cos(s(i,11)) * s(i,23) ^ 2 * l3 - (2 * F3) + 0.2e1 * m3 * g) / (m1 + m2 + m3) / 0.2e1; %EQ 4 C19 = (-0.4e1 * Jy1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) - 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C9 + 0.4e1 * Jx1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C2) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C20 = 0.4e1 * Jz1 * cos(s(i,5)) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C21 = (-0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C10 + m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) + m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C3) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C22 = (-0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C4 - m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) + m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) - 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C11) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C23 = (-0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C12 - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C5) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1

193 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C24 = (-0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C13 - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C6) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); C25 = (m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * s(i,17) * s(i,18) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) ^ 2 * s(i,16) * l1 ^ 2 * cos(s(i,5)) * s(i,17) - 0.8e1 * Jy1 * cos(s(i,6)) * sin(s(i,5)) ^ 2 * s(i,16) * sin(s(i,6)) * s(i,18) 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C7 + 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) - (4 * F4) - 0.4e1 * Jy1 * cos(s(i,6)) * cos(s(i,5)) * s(i,17) ^ 2 * sin(s(i,6)) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) + 0.4e1 * Jx1 * cos(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) - 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C14 - 0.8e1 * Jz1 * cos(s(i,5)) * s(i,16) * sin(s(i,5)) * s(i,17) + 0.4e1 * Jx1 * sin(s(i,6)) * cos(s(i,5)) * s(i,17) ^ 2 * cos(s(i,6)) + 0.8e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * s(i,16) * cos(s(i,5)) * s(i,17) - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) * s(i,17) * s(i,18) + 0.8e1 * Jx1 * sin(s(i,6)) * sin(s(i,5)) ^ 2 * s(i,16) * cos(s(i,6)) * s(i,18) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) ^ 2 * l1 ^ 2 * cos(s(i,5)) * s(i,17) * s(i,16) - m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.8e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) * s(i,16) * cos(s(i,5)) * s(i,17) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.4e1 * Jz1 * sin(s(i,5)) * s(i,17) * s(i,18)) / (-m1 * sin(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * C8 - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 - 0.4e1 * Jz1 * cos(s(i,5)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * C1 - m1 * sin(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2); %EQ 5 C26 = (-0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C20 - 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C20 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C20 + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C20) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); C27 = (-0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C3 + m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) - 0.2e1

194 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C21 - 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C21 - m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C21 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C21 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C10) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); C28 = (-0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C22 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C22 + m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C22 - 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C4 + 0.2e1 * m1 * sin(s(i,5)) * l1 * C16 + m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C22 + m1 * sin(s(i,5)) * l1 * sin(s(i,8)) * l2 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C11) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); C29 = (-0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C5 + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C23 - 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C23 - 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C23 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C23 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C12) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); C30 = (-0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C6 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C24 + 0.2e1 * m1 * sin(s(i,5)) * l1 * C17 - 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C24 + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C24 - 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C24 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C13) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) *

195 sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); C31 = (0.2e1 * m1 * g * sin(s(i,5)) * l1 + 0.4e1 * Jz1 * s(i,16) * sin(s(i,5)) * s(i,18) + 0.4e1 * Jz1 * s(i,16) ^ 2 * sin(s(i,5)) * cos(s(i,5)) + 0.2e1 * m1 * sin(s(i,5)) * l1 * C18 - (4 * F5) - m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - m1 * cos(s(i,5)) * cos(s(i,4)) ^ 2 * l1 ^ 2 * sin(s(i,5)) * s(i,17) ^ 2 - m1 * cos(s(i,5)) * sin(s(i,4)) ^ 2 * l1 ^ 2 * sin(s(i,5)) * s(i,17) ^ 2 - m1 * cos(s(i,5)) * cos(s(i,4)) ^ 2 * s(i,16) ^ 2 * l1 ^ 2 * sin(s(i,5)) - m1 * cos(s(i,5)) * sin(s(i,4)) ^ 2 * l1 ^ 2 * sin(s(i,5)) * s(i,16) ^ 2 - m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 - m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + m1 * sin(s(i,5)) * l1 * cos(s(i,8)) * s(i,20) ^ 2 * l2 + m1 * sin(s(i,5)) * l1 ^ 2 * cos(s(i,5)) * s(i,17) ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C14 - 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C25 - 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C7 - 0.8e1 * Jx1 * cos(s(i,6)) * s(i,17) * sin(s(i,6)) * s(i,18) + 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C25 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) + 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 * s(i,16) * sin(s(i,5)) * s(i,18) + 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C25 - 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C25 - 0.4e1 * Jx1 * s(i,16) ^ 2 * cos(s(i,5)) * sin(s(i,6)) ^ 2 * sin(s(i,5)) - 0.4e1 * Jy1 * s(i,16) ^ 2 * cos(s(i,5)) * cos(s(i,6)) ^ 2 * sin(s(i,5)) - 0.4e1 * Jx1 * sin(s(i,6)) ^ 2 * s(i,18) * s(i,16) * sin(s(i,5)) + 0.4e1 * Jx1 * cos(s(i,6)) ^ 2 * s(i,16) * sin(s(i,5)) * s(i,18) + 0.8e1 * Jy1 * sin(s(i,6)) * s(i,17) * cos(s(i,6)) * s(i,18) - 0.4e1 * Jy1 * cos(s(i,6)) ^ 2 * s(i,18) * s(i,16) * sin(s(i,5))) / (0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C2 - m1 * cos(s(i,5)) ^ 2 * sin(s(i,4)) ^ 2 * l1 ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * l1 * C15 - m1 * cos(s(i,5)) ^ 2 * cos(s(i,4)) ^ 2 * l1 ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * sin(s(i,4)) * l1 * C1 * C19 + 0.4e1 * Jy1 * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,6)) * C19 - 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C9 0.2e1 * m1 * cos(s(i,5)) * cos(s(i,4)) * l1 * C8 * C19 - 0.4e1 * Jx1 * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,6)) * C19 - m1 * sin(s(i,5)) ^ 2 * l1 ^ 2 - 0.4e1 * Jy1 * sin(s(i,6)) ^ 2 - 0.4e1 * Jx1 * cos(s(i,6)) ^ 2); %EQ6 C32 = -(Jz1 * cos(s(i,5)) * C19 * C27 + Jz1 * cos(s(i,5)) * C21) / Jz1 / (cos(s(i,5)) * C19 * C26 + cos(s(i,5)) * C20 + 0.1e1); C33 = -(Jz1 * cos(s(i,5)) * C22 + Jz1 * cos(s(i,5)) * C19 * C28) / Jz1 / (cos(s(i,5)) * C19 * C26 + cos(s(i,5)) * C20 + 0.1e1); C34 = -(Jz1 * cos(s(i,5)) * C23 + Jz1 * cos(s(i,5)) * C19 * C29) / Jz1 / (cos(s(i,5)) * C19 * C26 + cos(s(i,5)) * C20 + 0.1e1); C35 = -(Jz1 * cos(s(i,5)) * C19 * C30 + Jz1 * cos(s(i,5)) * C24) / Jz1 / (cos(s(i,5)) * C19 * C26 + cos(s(i,5)) * C20 + 0.1e1); C36 = -(-Jx1 * s(i,17) * cos(s(i,6)) ^ 2 * s(i,16) * sin(s(i,5)) + Jx1 * s(i,17) ^ 2 * cos(s(i,6)) * sin(s(i,6)) - F6 + Jx1 * s(i,16) * sin(s(i,5)) * sin(s(i,6)) ^ 2 * s(i,17) + Jz1 * cos(s(i,5)) * C19 * C31 - Jy1 * s(i,17) ^ 2 * cos(s(i,6)) * sin(s(i,6)) - Jz1 * s(i,16) * sin(s(i,5)) * s(i,17) - Jy1 * s(i,16) * sin(s(i,5)) * sin(s(i,6)) ^ 2 * s(i,17) + Jy1 * s(i,16) ^ 2 * sin(s(i,5)) ^ 2 * sin(s(i,6)) *

196 cos(s(i,6)) + Jz1 * cos(s(i,5)) * C25 - Jx1 * s(i,16) ^ 2 * sin(s(i,5)) ^ 2 * sin(s(i,6)) * cos(s(i,6)) + Jy1 * s(i,17) * cos(s(i,6)) ^ 2 * s(i,16) * sin(s(i,5))) / Jz1 / (cos(s(i,5)) * C19 * C26 + cos(s(i,5)) * C20 + 0.1e1); %EQ 7 C37 = -(0.4e1 * Jy2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) - 0.4e1 * Jx2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C28 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C33 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C22 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C33 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C22 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C33 m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C28 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C33 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C33 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C28 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C33 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C28 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C22 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C33 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C28 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C28 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C4 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C11 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C28 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C28 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C4 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C33 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C28 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C11) / (-m1 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m1 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(i,8)) ^ 2 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) *

197 cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32); C38 = 0.4e1 * Jz2 * cos(s(i,8)) / (-m1 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m1 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(i,8)) ^ 2 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) *

198 cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32); C39 = -(m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C29 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C23 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C23 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C34 - m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) - m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C29 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C29 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C34 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C34 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C34 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C29 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C34 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C34 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C29 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C5 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C34 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C29 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C34 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C23 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C34 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C34 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C23 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C29 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C34 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C23 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C29 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C12 - 0.2e1 * m3 * sin(s(i,8)) *

199 sin(s(i,7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C34 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C34 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C5 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C23 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C34 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C12) / (-m1 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m1 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(i,8)) ^ 2 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32); C40 = -(m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C35 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C35 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C35 + m1 *

200 sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C30 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C35 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C24 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C30 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C35 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C24 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C30 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C35 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C30 - m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C30 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C30 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C30 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C30 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C24 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C13 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C35 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C35 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C35 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C30 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C13 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C6 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C30 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C6 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C24 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C24 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C30 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C35 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C30 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C24 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C35 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C35) / (-m1 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m1 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(i,8)) ^ 2 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27

201 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32); C41 = -(0.4e1 * Jz2 * sin(s(i,8)) * s(i,20) * s(i,21) + (4 * F7) - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C31 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C36 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C36 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C31 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C25 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C36 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C36 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C31 - m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 + m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C25 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C36 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C31 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C36 + m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 - m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) + m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) - 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) - 0.8e1 * Jx2 * sin(s(i,9)) * sin(s(i,8)) ^ 2 * s(i,19) * cos(s(i,9)) * s(i,21) - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * s(i,23) * sin(s(i,10)) * s(i,22) - 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) ^ 2 * s(i,19) * l2 ^ 2 * cos(s(i,8)) * s(i,20) - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) ^ 2 * l2 ^ 2 * cos(s(i,8)) * s(i,20) * s(i,19) - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) ^ 2 * s(i,19) * l2 ^ 2 * cos(s(i,8)) *

202 s(i,20) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C25 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C31 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C36 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C31 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C31 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C7 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C25 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C31 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C36 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C7 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C36 - 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) ^ 2 * l2 ^ 2 * cos(s(i,8)) * s(i,20) * s(i,19) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C31 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C25 + 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) * s(i,20) * s(i,21) + 0.8e1 * Jz2 * cos(s(i,8)) * s(i,19) * sin(s(i,8)) * s(i,20) + 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * s(i,20) * s(i,21) - 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) - 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) + 0.4e1 * Jy2 * cos(s(i,9)) * cos(s(i,8)) * s(i,20) ^ 2 * sin(s(i,9)) - 0.8e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * s(i,19) * cos(s(i,8)) * s(i,20) - 0.8e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) * s(i,19) * cos(s(i,8)) * s(i,20) + 0.8e1 * Jy2 * cos(s(i,9)) * sin(s(i,8)) ^ 2 * s(i,19) * sin(s(i,9)) * s(i,21) - 0.4e1 * Jx2 * sin(s(i,9)) * cos(s(i,8)) * s(i,20) ^ 2 * cos(s(i,9)) - 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * s(i,23) * cos(s(i,10)) * s(i,22) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C36 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C14 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C36 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C14 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C31 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C25) / (-m1 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 - m1 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - m3 * sin(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 - 0.4e1 * Jz2 * cos(s(i,8)) ^ 2 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 - m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 - m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 + m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 - m1 * sin(s(i,8)) * sin(s(i,7)) *

203 l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C10 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C20 * C32 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C20 * C32 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C1 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C19 * C27 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C8 * C21 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C3 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C27 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * C2 * C26 * C32 - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * C9 * C26 * C32); %EQ 8 C42 = -(m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C38 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C38 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C38 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C38 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C38 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C38 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C38 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C38 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C38 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C38 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C38 + 0.2e1 * m1 *

204 cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C38 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C38 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C38 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C38 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C38 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C38 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C38 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C38 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C38) / (m3 * sin(s(i,8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 + 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 + m1 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m1 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C16 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C16 + m1 * sin(s(i,8)) ^ 2 * l2 ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C22 m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C22 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C28 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C28 m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C33 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) *

205 sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C37 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37

206 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37); C43 = -(m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C29 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C39 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C39 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C39 + m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C39 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C23 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C39 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C34 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C34 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C39 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C34 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C34 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C29 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C29 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C39 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C34 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C34 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C34 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C23 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C39 - m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C39 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C39 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C39 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C29 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C39 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C39 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C29 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C34 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C29 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C39 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C34 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C5 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C29 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C34 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C34 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 *

207 C32 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C39 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C5 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C34 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C39 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C23 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C23 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C12 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C29 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C34 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C39 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C29 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C34 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C34 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C29 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C34 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C29 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C29 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C23 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C39 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C39 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C34 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C29 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C12 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C34 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C34 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C39 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C39 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C39 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C23 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C39 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C34 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C29 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C39 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C39 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C29) / (m3 * sin(s(i,8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 + 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 + m1 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m1 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C16 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C16 + m1 * sin(s(i,8)) ^ 2 * l2 ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C22 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C22 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) *

208 sin(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C28 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C33 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 *

209 cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C37 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37); C44 = -(-0.2e1 * m3 * sin(s(i,8)) * l2 * C17 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C17 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C40 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C35 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C40 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C40 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C30 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C30 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C40 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C40 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C40 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C30 + m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C24 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C35 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C40 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C35 + m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C35 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C30 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C40 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C40 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C30 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C40 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) *

210 cos(s(i,4)) * C24 + m3 * sin(s(i,8)) * l2 * sin(s(i,11)) * l3 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C35 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C40 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C35 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C40 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C35 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C40 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C40 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C13 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C30 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C30 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C24 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C30 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C35 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C6 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C30 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C13 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C24 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C30 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C6 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C35 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C35 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C40 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C35 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C24 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C40 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C24 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C40 - 0.2e1 * m1 *

211 cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C30 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C40 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C30 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C35 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C30 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C40 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C40 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C35) / (m3 * sin(s(i,8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 + 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 + m1 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m1 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C16 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C16 + m1 * sin(s(i,8)) ^ 2 * l2 ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C22 m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C22 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C28 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C28 m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C33 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 *

212 C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C37 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37); C45 = -(-0.2e1 * m3 * g * sin(s(i,8)) * l2 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C18 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C18 + 0.2e1 * m1 * g * sin(s(i,8)) * l2 + 0.4e1 * Jz2 * s(i,19) ^ 2 * sin(s(i,8)) *

213 cos(s(i,8)) + 0.4e1 * Jz2 * s(i,19) * sin(s(i,8)) * s(i,21) - (4 * F8) + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C31 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C31 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C36 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C41 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C36 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C41 - m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 - m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + m1 * sin(s(i,8)) * l2 * cos(s(i,5)) * s(i,17) ^ 2 * l1 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C41 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C36 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C41 - m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C41 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C41 m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C41 - m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C25 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C31 + m3 * sin(s(i,8)) * l2 ^ 2 * cos(s(i,8)) * s(i,20) ^ 2 + m3 * sin(s(i,8)) * l2 * cos(s(i,11)) * s(i,23) ^ 2 * l3 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C31 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C41 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C41 - m3 * cos(s(i,8)) * cos(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,20) ^ 2 - m1 * cos(s(i,8)) * sin(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,20) ^ 2 - m3 * cos(s(i,8)) * sin(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,20) ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,20) ^ 2 - m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - m1 * cos(s(i,8)) * cos(s(i,7)) ^ 2 * s(i,19) ^ 2 * l2 ^ 2 * sin(s(i,8)) m1 * cos(s(i,8)) * sin(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,19) ^ 2 - m3 * cos(s(i,8)) * cos(s(i,7)) ^ 2 * s(i,19) ^ 2 * l2 ^ 2 * sin(s(i,8)) - m3 * cos(s(i,8)) * sin(s(i,7)) ^ 2 * l2 ^ 2 * sin(s(i,8)) * s(i,19) ^ 2 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C31 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C41 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C36 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C41 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C41 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C36 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C36 + m1 * sin(s(i,8)) * l2 ^ 2 * cos(s(i,8)) * s(i,20) ^ 2 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C41 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C36 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C41 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C25 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * l3 *

214 cos(s(i,11)) * s(i,23) * sin(s(i,10)) * s(i,22) - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C7 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C14 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C36 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C31 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C25 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C36 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C41 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C41 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C41 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C25 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C41 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C36 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C25 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C31 - 0.4e1 * Jy2 * s(i,19) ^ 2 * cos(s(i,8)) * cos(s(i,9)) ^ 2 * sin(s(i,8)) + 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 * s(i,19) * sin(s(i,8)) * s(i,21) + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C36 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C36 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C31 + 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 * s(i,19) * sin(s(i,8)) * s(i,21) + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * s(i,23) * cos(s(i,10)) * s(i,22) - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C31 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C36 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C41 + 0.8e1 * Jy2 * sin(s(i,9)) * s(i,20) * cos(s(i,9)) * s(i,21) - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C31 + 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) - 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C31 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C31 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C36 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C41 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C36 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C36 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C41 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C41 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C41 - 0.4e1 * Jx2 * sin(s(i,9)) ^ 2 * s(i,21) * s(i,19) * sin(s(i,8)) - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C41 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C41 - 0.4e1 * Jx2 * s(i,19) ^ 2 * cos(s(i,8)) * sin(s(i,9)) ^ 2 * sin(s(i,8)) - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C14 - 0.8e1 * Jx2 * cos(s(i,9)) * s(i,20) * sin(s(i,9)) * s(i,21) - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C31 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C31 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C36 + 0.2e1 * m1 * sin(s(i,8)) * l2 *

215 C15 * C27 * C41 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C31 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C36 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C41 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C7 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C41 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C25 - 0.4e1 * Jy2 * cos(s(i,9)) ^ 2 * s(i,21) * s(i,19) * sin(s(i,8)) - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C36 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C41 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C41 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C41) / (m3 * sin(s(i,8)) ^ 2 * l2 ^ 2 + 0.4e1 * Jx2 * cos(s(i,9)) ^ 2 + 0.4e1 * Jy2 * sin(s(i,9)) ^ 2 + m1 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m1 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * cos(s(i,7)) ^ 2 * l2 ^ 2 + m3 * cos(s(i,8)) ^ 2 * sin(s(i,7)) ^ 2 * l2 ^ 2 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C16 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C16 + m1 * sin(s(i,8)) ^ 2 * l2 ^ 2 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C22 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C22 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C28 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C28 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C33 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C33 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C21 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C27 * C37 + m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * C26 * C32 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C27 * C37 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C33 + m1 * sin(s(i,8)) * l2 * sin(s(i,5)) * l1 * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * C26 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C20 * C32 * C37 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C26 * C33 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C20 * C32 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C19 * C28 - m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * C19 * C27 * C37 + m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 *

216 C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C32 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C22 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C3 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C22 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C33 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C21 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C27 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C28 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C4 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 + 0.4e1 * Jx2 * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,9)) * C37 - 0.4e1 * Jy2 * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,9)) * C37 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C27 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C10 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C9 * C26 * C33 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C21 * C37 - 0.2e1 * m3 * cos(s(i,8)) * cos(s(i,7)) * l2 * C11 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C27 * C37 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C28 - 0.2e1 * m3 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C27 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C33 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C20 * C32 * C37 + 0.2e1 * m1 * sin(s(i,8)) * l2 * C15 * C26 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C27 * C37 0.2e1 * m1 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 * C37 + 0.2e1 * m1 * cos(s(i,8)) * cos(s(i,7)) * l2 * C8 * C19 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C2 * C26 * C32 * C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C20 * C32 *

217 C37 + 0.2e1 * m3 * cos(s(i,8)) * sin(s(i,7)) * l2 * C1 * C19 * C27 * C37); %EQ 9 C46 = (-Jz2 * cos(s(i,8)) * C37 * C43 - Jz2 * cos(s(i,8)) * C39) / Jz2 / (cos(s(i,8)) * C37 * C42 + cos(s(i,8)) * C38 + 0.1e1); C47 = (-Jz2 * cos(s(i,8)) * C40 - Jz2 * cos(s(i,8)) * C37 * C44) / Jz2 / (cos(s(i,8)) * C37 * C42 + cos(s(i,8)) * C38 + 0.1e1); C48 = (Jy2 * s(i,19) * sin(s(i,8)) * sin(s(i,9)) ^ 2 * s(i,20) - Jz2 * cos(s(i,8)) * C41 - Jz2 * cos(s(i,8)) * C37 * C45 + Jx2 * s(i,19) ^ 2 * sin(s(i,8)) ^ 2 * sin(s(i,9)) * cos(s(i,9)) - Jx2 * s(i,19) * sin(s(i,8)) * sin(s(i,9)) ^ 2 * s(i,20) + Jx2 * s(i,20) * cos(s(i,9)) ^ 2 * s(i,19) * sin(s(i,8)) + Jz2 * s(i,19) * sin(s(i,8)) * s(i,20) - Jy2 * s(i,19) ^ 2 * sin(s(i,8)) ^ 2 * sin(s(i,9)) * cos(s(i,9)) - Jy2 * s(i,20) * cos(s(i,9)) ^ 2 * s(i,19) * sin(s(i,8)) + Jy2 * s(i,20) ^ 2 * cos(s(i,9)) * sin(s(i,9)) - Jx2 * s(i,20) ^ 2 * cos(s(i,9)) * sin(s(i,9)) + F9) / Jz2 / (cos(s(i,8)) * C37 * C42 + cos(s(i,8)) * C38 + 0.1e1); %EQ 10 C49 = (0.4e1 * Jy3 * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,12)) - 0.4e1 * Jx3 * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,12)) - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C44 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C40 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C47 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C47 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C47 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C47 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C40 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C44 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C47 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C47 m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C44 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C40 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C44 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C44 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 *

218 C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C35 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C40 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C6 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C30 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C30 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C47 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C40 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C40 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C44 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C24 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C47 - 0.2e1 *

219 m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C30 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C13 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C24 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C30 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C35) / (m3 * sin(s(i,11)) ^ 2 * sin(s(i,10)) ^ 2 * l3 ^ 2 + m3 * sin(s(i,11)) ^ 2 * cos(s(i,10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + 0.4e1 * Jz3 * cos(s(i,11)) ^ 2 + 0.4e1 * Jx3 * sin(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 *

220 sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C12 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C5 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) *

221 l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C29 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C39); C50 = -0.4e1 * Jz3 * cos(s(i,11)) / (m3 * sin(s(i,11)) ^ 2 * sin(s(i,10)) ^ 2 * l3 ^ 2 + m3 * sin(s(i,11)) ^ 2 * cos(s(i,10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + 0.4e1 * Jz3 * cos(s(i,11)) ^ 2 + 0.4e1 * Jx3 * sin(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10))

222 * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C12 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C5 + 0.2e1

223 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C29 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C39); C51 = (0.4e1 * Jz3 * sin(s(i,11)) * s(i,23) * s(i,24) + (4 * F10) - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C48 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C45 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C48 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C48 m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C45 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C45 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C41 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C48 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C48 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C48 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C41 - m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 *

224 sin(s(i,8)) * cos(s(i,7)) * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C45 0.8e1 * Jx3 * sin(s(i,12)) ^ 2 * sin(s(i,11)) * s(i,22) * cos(s(i,11)) * s(i,23) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C45 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C41 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C7 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C45 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C38 * C48 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C38 * C48 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C42 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C42 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C36 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C41 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C36 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C36 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C31 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C45 - 0.2e1 * m3 *

225 sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C41 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C31 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C41 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) ^ 2 * l3 ^ 2 * cos(s(i,11)) * s(i,23) * s(i,22) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) ^ 2 * s(i,22) * l3 ^ 2 * cos(s(i,11)) * s(i,23) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C41 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C38 * C48 + 0.8e1 * Jz3 * cos(s(i,11)) * s(i,22) * sin(s(i,11)) * s(i,23) 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C14 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C36 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C36 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C45 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C48 + 0.4e1 * Jx3 * sin(s(i,12)) ^ 2 * sin(s(i,11)) * s(i,23) * s(i,24) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C45 - 0.4e1 * Jx3 * cos(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) - 0.4e1 * Jy3 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C41 - 0.4e1 * Jx3 * sin(s(i,12)) * cos(s(i,11)) * s(i,23) ^ 2 * cos(s(i,12)) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C31 + 0.4e1 * Jy3 * cos(s(i,12)) * cos(s(i,11)) * s(i,23) ^ 2 * sin(s(i,12)) + 0.4e1 * Jy3 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * s(i,23) * s(i,24) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C48 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C45 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C38 * C48 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C41 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C48 - 0.8e1 * Jx3 * sin(s(i,12)) * sin(s(i,11)) ^ 2 * s(i,22) * cos(s(i,12)) * s(i,24) + 0.8e1 * Jy3 * cos(s(i,12)) * sin(s(i,11)) ^ 2 * s(i,22) * sin(s(i,12)) * s(i,24) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C25 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C31 - 0.8e1 * Jy3 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * s(i,22) *

226 cos(s(i,11)) * s(i,23) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C41 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C45 - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C45 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C25 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C41) / (m3 * sin(s(i,11)) ^ 2 * sin(s(i,10)) ^ 2 * l3 ^ 2 + m3 * sin(s(i,11)) ^ 2 * cos(s(i,10)) ^ 2 * l3 ^ 2 + 0.4e1 * Jy3 * cos(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + 0.4e1 * Jz3 * cos(s(i,11)) ^ 2 + 0.4e1 * Jx3 * sin(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 + m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 - m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 + m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C28 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C12 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3

227 * C8 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C26 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C19 * C27 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C9 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C5 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C32 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C21 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C23 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C23 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C2 * C29 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C4 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C21 * C39 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C3 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C20 * C34 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C37 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C8 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C22 * C43 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C10 * C38 * C46 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * C1 * C19 * C29 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * C11 * C42 * C46 + 0.2e1 * m3 *

228 sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11)) sin(s(i,11))

* * * * * * * * * * * *

cos(s(i,10)) sin(s(i,10)) sin(s(i,10)) cos(s(i,10)) sin(s(i,10)) cos(s(i,10)) cos(s(i,10)) cos(s(i,10)) sin(s(i,10)) sin(s(i,10)) sin(s(i,10)) cos(s(i,10))

* * * * * * * * * * * *

l3 l3 l3 l3 l3 l3 l3 l3 l3 l3 l3 l3

* * * * * * * * * * * *

C4 * C42 * C46 + 0.2e1 C9 * C26 * C34 + 0.2e1 C9 * C27 * C39 + 0.2e1 C2 * C27 * C39 + 0.2e1 C8 * C19 * C29 + 0.2e1 C1 * C21 * C39 + 0.2e1 C2 * C26 * C34 + 0.2e1 C2 * C28 * C43 + 0.2e1 C9 * C28 * C43 + 0.2e1 C11 * C43 + 0.2e1 * m3 C10 * C39 + 0.2e1 * m3 C3 * C39);

* * * * * * * * * * *

m3 m3 m3 m3 m3 m3 m3 m3 m3

* * * * * * * * *

%EQ 11 C52 = (-m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 * C50 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 * C50 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 * C50 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 * C50 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 * C50 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 * C50 m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 * C50 - m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C43 * C50 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 * C50 - m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C46 * C50 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 * C50 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 * C50 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 * C50 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C29 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C12 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C5 * C50 + 0.4e1 * Jy3 * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,12)) * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C29 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C39 * C50 - 0.4e1 * Jx3 * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,12)) * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C34 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C29 * C50 - 0.2e1 * m3 * cos(s(i,11)) *

229 sin(s(i,10)) * l3 * C2 * C28 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C34 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C29 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C43 * C50 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 * C50 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C23 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C23 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C43 *

230 C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C43 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 * C50 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C39 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C29 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C34 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C43 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C43 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C39 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C50 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C34 * C50 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C50 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C46 * C50) / (m3 * cos(s(i,11)) ^ 2 * sin(s(i,10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C17 + m3 * sin(s(i,11)) ^ 2 * l3 ^ 2 + m3 * cos(s(i,11)) ^ 2 * cos(s(i,10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C13 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C44 + 0.4e1 * Jx3 * cos(s(i,12)) ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C29 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C47 - 0.2e1 * m3 *

231 sin(s(i,11)) * l3 * C16 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C30 + 0.4e1 * Jx3 * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,12)) * C49 - 0.4e1 * Jy3 * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,12)) * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C6 + 0.4e1 * Jy3 * sin(s(i,12)) ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C44 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C47 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C46 * C49 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C44 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C43 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C40 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C44 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C44 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C47 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C40 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C44 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 * C49 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 * C49 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C47 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C44 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C44 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C47 -

232 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C39 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C46 * C49 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C34 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C24 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C44 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C12 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C47 + 0.2e1 *

233 m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C24 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C29 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C23 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C35 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 *

234 C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C40 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C23 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C5 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 * C49 +

235 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C40); C53 = (0.2e1 * m3 * g * sin(s(i,11)) * l3 + 0.4e1 * Jx3 * s(i,22) ^ 2 * cos(s(i,11)) * sin(s(i,12)) ^ 2 * sin(s(i,11)) + 0.4e1 * Jy3 * s(i,22) ^ 2 * cos(s(i,11)) * cos(s(i,12)) ^ 2 * sin(s(i,11)) + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C14 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C5 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C39 * C51 - 0.4e1 * Jz3 * s(i,22) * sin(s(i,11)) * s(i,24) - 0.8e1 * Jy3 * sin(s(i,12)) * s(i,23) * cos(s(i,12)) * s(i,24) + 0.2e1 * m3 * sin(s(i,11)) * l3 * C18 - 0.4e1 * Jz3 * s(i,22) ^ 2 * sin(s(i,11)) * cos(s(i,11)) + 0.8e1 * Jx3 * cos(s(i,12)) * s(i,23) * sin(s(i,12)) * s(i,24) + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C34 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C45 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C7 + (4 * F11) - m3 * sin(s(i,11)) * l3 * cos(s(i,8)) * s(i,20) ^ 2 * l2 - m3 * sin(s(i,11)) * l3 ^ 2 * cos(s(i,11)) * s(i,23) ^ 2 + m3 * cos(s(i,11)) * sin(s(i,10)) ^ 2 * l3 ^ 2 * sin(s(i,11)) * s(i,23) ^ 2 + m3 * cos(s(i,11)) * cos(s(i,10)) ^ 2 * l3 ^ 2 * sin(s(i,11)) * s(i,23) ^ 2 + m3 * cos(s(i,11)) * cos(s(i,10)) ^ 2 * s(i,22) ^ 2 * l3 ^ 2 * sin(s(i,11)) + m3 * cos(s(i,11)) * sin(s(i,10)) ^ 2 * l3 ^ 2 * sin(s(i,11)) * s(i,22) ^ 2 - m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C46 * C51 - m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C48 - m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C43 * C51 - m3 *

236 sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C45 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C41 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 * C51 m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C45 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 * C51 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C48 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C45 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C41 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 * C51 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 * C51 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C48 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 * C51 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C48 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 * C51 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 * C51 m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C48 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 * C51 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C45 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C48 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 * C51 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C48 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C45 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 * C51 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 * C51 - m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 * C51 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C31 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C41 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C34 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C46 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C46 * C51 - 0.4e1 * Jy3 * sin(s(i,12)) ^ 2 * s(i,22) * sin(s(i,11)) * s(i,24) + 0.4e1 * Jy3 * cos(s(i,12)) ^ 2 * s(i,24) * s(i,22) * sin(s(i,11)) + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C31 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 *

237 C28 * C43 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C45 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C39 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C29 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C36 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C43 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C45 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C45 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C45 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C41 + 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C43 * C51 + 0.4e1 * Jy3 * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,12)) * C51 - 0.4e1 * Jx3 * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,12)) * C51 - 0.4e1 * Jx3 * cos(s(i,12)) ^ 2 * s(i,22) * sin(s(i,11)) * s(i,24) + 0.4e1 * Jx3 * sin(s(i,12)) ^ 2 * s(i,24) * s(i,22) * sin(s(i,11)) - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 * C51 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C25 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C25 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C36 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C36 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C43 * C51 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C41 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C41 - 0.2e1

238 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C41 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C48 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C39 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C39 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C41 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C41 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C34 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C36 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C45 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C31 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C36 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C45 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 *

239 C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C34 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C12 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C34 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C29 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C31 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C31 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C23 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C34 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C29 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C43 * C51 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C41 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C36 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C23 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C29 * C51 + 0.2e1 * m3 *

240 cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C45 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C34 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C39 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C41 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C29 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C41 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C36 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 * C51 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C45 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C48 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C45 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C43 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C39 * C51 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C43 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C39 * C51 - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C48 + 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19)) / (m3 * cos(s(i,11)) ^ 2 * sin(s(i,10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C17 + m3 * sin(s(i,11)) ^ 2 * l3 ^ 2 + m3 * cos(s(i,11)) ^ 2 * cos(s(i,10)) ^ 2 * l3 ^ 2 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C13 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C40 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C44 +

241 0.4e1 * Jx3 * cos(s(i,12)) ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C29 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C44 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C35 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C30 + 0.4e1 * Jx3 * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,12)) * C49 - 0.4e1 * Jy3 * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,12)) * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C6 + 0.4e1 * Jy3 * sin(s(i,12)) ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C44 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C47 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C42 * C46 * C49 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C44 + m3 * sin(s(i,11)) * l3 * sin(s(i,8)) * l2 * C43 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C40 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C46 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C44 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C44 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C47 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C40 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C44 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C42 * C46 * C49 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C46 * C49 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C42 * C47 + m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * C43 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C39 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C37 * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C46 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * C42 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C39 * C49 - m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * C38 * C46 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C42 * C47 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C43 * C49 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C37 * C44 + m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C43 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 *

242 cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C44 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C47 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C44 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C39 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C47 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C16 * C42 * C46 * C49 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C40 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C34 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C28 * C42 * C46 * C49 - 0.2e1 * m3 * sin(s(i,11)) * l3 * C15 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C43 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C24 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C44 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C12 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 *

243 C8 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C24 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C29 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C29 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C23 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C22 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C40 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C35 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 *

244 C32 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C33 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C11 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C39 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C28 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C30 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C34 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C40 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C23 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C27 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C10 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C42 * C47 + 0.2e1 * m3 *

245 cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C28 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C5 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C3 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C4 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C34 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C44 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C27 * C37 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C32 * C38 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C38 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C27 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C26 * C32 * C37 * C42 * C46 * C49 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C28 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C33 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C20 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C43 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C21 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C33 * C42 * C46 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C19 * C30 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C20 * C35 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C42 * C47 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C37 * C43 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C21 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C8 * C19 * C26 * C32 * C38 * C46 * C49 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C40 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C1 * C22 * C42 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C37 * C44 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C38 * C47 - 0.2e1 * m3 * cos(s(i,11)) * cos(s(i,10)) * l3 * C9 * C26 * C32 * C39 * C49 + 0.2e1 * m3 * cos(s(i,11)) * sin(s(i,10)) * l3 * C2 * C26 * C32 * C40); %EQ 12 C54 = (-Jz3 * cos(s(i,11)) * C49 * C53 - Jz3 * cos(s(i,11)) * C51 + Jz3 * s(i,22) * sin(s(i,11)) * s(i,23) + Jx3 * s(i,22) ^ 2 * sin(s(i,11)) ^ 2 * sin(s(i,12)) * cos(s(i,12)) - Jx3 * s(i,22) * sin(s(i,11)) * sin(s(i,12)) ^ 2 * s(i,23) + Jx3 * s(i,23) * cos(s(i,12)) ^ 2 * s(i,22) * sin(s(i,11)) - Jx3 * s(i,23) ^ 2 * cos(s(i,12)) * sin(s(i,12)) - Jy3 * s(i,22) ^ 2 * sin(s(i,11)) ^ 2 * sin(s(i,12)) * cos(s(i,12)) - Jy3 * s(i,23) * cos(s(i,12)) ^ 2 * s(i,22) * sin(s(i,11)) + Jy3 * s(i,22) * sin(s(i,11)) * sin(s(i,12)) ^ 2 * s(i,23) + Jy3 * s(i,23) ^ 2 * cos(s(i,12)) * sin(s(i,12)) + F12) / Jz3 / (cos(s(i,11)) * C49 * C52 + cos(s(i,11)) * C50 + 0.1e1);

246

Rotation Matrices – Rotations.m %This function calculations the rotations at each time step %Variable Description % R = Rotation Matrix defined in Mierovich % RT = Transpose of R % Rdot = d/dt of R % RTdot = Transpose of Rdot %These are written in 'for loop' form because the rotation matrix changes with each time step %All Rotations are 3x3 Matrices function [R1, RT1, Rdot1, RTdot1, R2, RT2, Rdot2, RTdot2, R3, RT3, Rdot3, RTdot3] = Rotations (s, i) %Link 1 R1 = [cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) cos(s(i,6)) * sin(s(i,4)) + sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) sin(s(i,6)) * sin(s(i,5)); -sin(s(i,6)) * cos(s(i,4)) cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) -sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) cos(s(i,6)) * sin(s(i,5)); sin(s(i,5)) * sin(s(i,4)) -sin(s(i,5)) * cos(s(i,4)) cos(s(i,5));]; RT1 = [cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) -sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) sin(s(i,5)) * sin(s(i,4)); cos(s(i,6)) * sin(s(i,4)) + sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) -sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) -sin(s(i,5)) * cos(s(i,4)); sin(s(i,6)) * sin(s(i,5)) cos(s(i,6)) * sin(s(i,5)) cos(s(i,5));]; Rdot1 = [(-cos(s(i,6)) * sin(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,16) + sin(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * s(i,17) + (-sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,18) (cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,16) - sin(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * s(i,17) + (-sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,18) sin(s(i,6)) * cos(s(i,5)) * s(i,17) + cos(s(i,6)) * sin(s(i,5)) * s(i,18); (sin(s(i,6)) * sin(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,16) + cos(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * s(i,17) + (-cos(s(i,6)) * cos(s(i,4)) + sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,18) (sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,16) - cos(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * s(i,17) + (cos(s(i,6)) * sin(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,18) cos(s(i,6)) * cos(s(i,5)) * s(i,17) - sin(s(i,6)) * sin(s(i,5)) * s(i,18); sin(s(i,5)) * cos(s(i,4)) * s(i,16) + cos(s(i,5)) * sin(s(i,4)) * s(i,17) sin(s(i,5)) * sin(s(i,4)) * s(i,16) - cos(s(i,5)) * cos(s(i,4)) * s(i,17) -sin(s(i,5)) * s(i,17);]; RTdot1 = [(-cos(s(i,6)) * sin(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,16) + sin(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * s(i,17) + (-sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,18) (sin(s(i,6)) * sin(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,16) + cos(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * s(i,17) + (-cos(s(i,6)) * cos(s(i,4)) + sin(s(i,6)) *

247 cos(s(i,5)) * sin(s(i,4))) * s(i,18) sin(s(i,5)) * cos(s(i,4)) * s(i,16) + cos(s(i,5)) * sin(s(i,4)) * s(i,17); (cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,16) sin(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * s(i,17) + (-sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,18) (sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * s(i,16) - cos(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * s(i,17) + (cos(s(i,6)) * sin(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * s(i,18) sin(s(i,5)) * sin(s(i,4)) * s(i,16) - cos(s(i,5)) * cos(s(i,4)) * s(i,17); sin(s(i,6)) * cos(s(i,5)) * s(i,17) + cos(s(i,6)) * sin(s(i,5)) * s(i,18) cos(s(i,6)) * cos(s(i,5)) * s(i,17) - sin(s(i,6)) * sin(s(i,5)) * s(i,18) -sin(s(i,5)) * s(i,17);]; %Link 2 R2 = [cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) sin(s(i,9)) * sin(s(i,8)); -sin(s(i,9)) * cos(s(i,7)) cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) -sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) cos(s(i,9)) * sin(s(i,8)); sin(s(i,8)) * sin(s(i,7)) -sin(s(i,8)) * cos(s(i,7)) cos(s(i,8));]; RT2 = [cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) -sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) sin(s(i,8)) * sin(s(i,7)); cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) -sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) -sin(s(i,8)) * cos(s(i,7)); sin(s(i,9)) * sin(s(i,8)) cos(s(i,9)) * sin(s(i,8)) cos(s(i,8));]; Rdot2 = [(-cos(s(i,9)) * sin(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,19) + sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * s(i,20) + (-sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,21) (cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,19) - sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * s(i,20) + (-sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,21) sin(s(i,9)) * cos(s(i,8)) * s(i,20) + cos(s(i,9)) * sin(s(i,8)) * s(i,21); (sin(s(i,9)) * sin(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,19) + cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * s(i,20) + (-cos(s(i,9)) * cos(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,21) (sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,19) - cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * s(i,20) + (cos(s(i,9)) * sin(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,21) cos(s(i,9)) * cos(s(i,8)) * s(i,20) - sin(s(i,9)) * sin(s(i,8)) * s(i,21); sin(s(i,8)) * cos(s(i,7)) * s(i,19) + cos(s(i,8)) * sin(s(i,7)) * s(i,20) sin(s(i,8)) * sin(s(i,7)) * s(i,19) - cos(s(i,8)) * cos(s(i,7)) * s(i,20) -sin(s(i,8)) * s(i,20);]; RTdot2 = [(-cos(s(i,9)) * sin(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,19) + sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * s(i,20) + (-sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,21) (sin(s(i,9)) * sin(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,19) + cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * s(i,20) + (-cos(s(i,9)) * cos(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,21) sin(s(i,8)) * cos(s(i,7)) * s(i,19) + cos(s(i,8)) * sin(s(i,7)) * s(i,20); (cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,19) sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * s(i,20) + (-sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,21) (sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * s(i,19) - cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * s(i,20) + (-

248 cos(s(i,9)) * sin(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * s(i,21) sin(s(i,8)) * sin(s(i,7)) * s(i,19) - cos(s(i,8)) * cos(s(i,7)) * s(i,20); sin(s(i,9)) * cos(s(i,8)) * s(i,20) + cos(s(i,9)) * sin(s(i,8)) * s(i,21) cos(s(i,9)) * cos(s(i,8)) * s(i,20) - sin(s(i,9)) * sin(s(i,8)) * s(i,21) -sin(s(i,8)) * s(i,20);]; %Link 3 R3 = [cos(s(i,12)) * cos(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) cos(s(i,12)) * sin(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) sin(s(i,12)) * sin(s(i,11)); -sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) -sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) cos(s(i,12)) * sin(s(i,11)); sin(s(i,11)) * sin(s(i,10)) -sin(s(i,11)) * cos(s(i,10)) cos(s(i,11));]; RT3 = [cos(s(i,12)) * cos(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) -sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) sin(s(i,11)) * sin(s(i,10)); cos(s(i,12)) * sin(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) -sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) -sin(s(i,11)) * cos(s(i,10)); sin(s(i,12)) * sin(s(i,11)) cos(s(i,12)) * sin(s(i,11)) cos(s(i,11));]; Rdot3 = [(-cos(s(i,12)) * sin(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,22) + sin(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * s(i,23) + (-sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,24) (cos(s(i,12)) * cos(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,22) - sin(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * s(i,23) + (-sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,24) sin(s(i,12)) * cos(s(i,11)) * s(i,23) + cos(s(i,12)) * sin(s(i,11)) * s(i,24); (sin(s(i,12)) * sin(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,22) + cos(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * s(i,23) + (-cos(s(i,12)) * cos(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,24) (sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,22) - cos(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * s(i,23) + (-cos(s(i,12)) * sin(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,24) cos(s(i,12)) * cos(s(i,11)) * s(i,23) sin(s(i,12)) * sin(s(i,11)) * s(i,24); sin(s(i,11)) * cos(s(i,10)) * s(i,22) + cos(s(i,11)) * sin(s(i,10)) * s(i,23) sin(s(i,11)) * sin(s(i,10)) * s(i,22) - cos(s(i,11)) * cos(s(i,10)) * s(i,23) sin(s(i,11)) * s(i,23);]; RTdot3 = [(-cos(s(i,12)) * sin(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,22) + sin(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * s(i,23) + (-sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,24) (sin(s(i,12)) * sin(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,22) + cos(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * s(i,23) + (-cos(s(i,12)) * cos(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,24) sin(s(i,11)) * cos(s(i,10)) * s(i,22) + cos(s(i,11)) * sin(s(i,10)) * s(i,23); (cos(s(i,12)) * cos(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,22) sin(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * s(i,23) + (-sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,24) (sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) * s(i,22) - cos(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * s(i,23) + (-cos(s(i,12)) * sin(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) * s(i,24) sin(s(i,11)) * sin(s(i,10)) * s(i,22) cos(s(i,11)) * cos(s(i,10)) * s(i,23); sin(s(i,12)) * cos(s(i,11)) * s(i,23) + cos(s(i,12)) * sin(s(i,11)) * s(i,24) cos(s(i,12)) *

249 cos(s(i,11)) * s(i,23) - sin(s(i,12)) * sin(s(i,11)) * s(i,24) sin(s(i,11)) * s(i,23);];

COM Kinematics – COM.m %This function calculaties the kinematics of links 1, 3 and the %system's COM %Format -> X = [x1,y1,z1,x2,y2,z2,x3,y3,z3,xs,ys,zs] % V = [x1,y1,z1,x2,y2,z2,x3,y3,z3,xs,ys,zs] % JOINT = [xj1,yj1,zj1,xj2,yj2,zj2] function [X,V,JOINT] = COM (s) %Read Constants Constants; % Size of s - Variable for the lenght of the loop [m n] = size(s); %Initialize the variables X = zeros(m,12); V = zeros(m,12); JOINT = zeros(m,6); %Loop for all rows in s for i=1:m %Calculate the rotation matrices for this time step - Rotations.m [R1, RT1, Rdot1, RTdot1, R2, RT2, Rdot2, RTdot2, R3, RT3, Rdot3, RTdot3] = Rotations (s, i); %Link 1 X(i,1:3) = (s(i,1:3)' - RT2*[0 0 l2/2]' - RT1*[0 0 l1/2]')'; V(i,1:3) = (s(i,13:15)' - RTdot2*[0 0 l2/2]' - RTdot1*[0 0 l1/2]')'; %Link 2 X(i,4:6) = s(i,1:3); V(i,4:6) = s(i,13:15); %Link 3 X(i,7:9) = (s(i,1:3)' + RT2*[0 0 l2/2]' + RT3*[0 0 l3/2]')'; V(i,7:9) = (s(i,13:15)' + RTdot2*[0 0 l2/2]' + RTdot3*[0 0 l3/2]')'; %System COM - Position for j = 1:3 X(i,j+9) = (m1*X(i,j) + m2*X(i,3+j) + m3*X(i,6+j))/(m1+m2+m3); end %System COM - Velocity for j = 1:3 V(i,j+9) = (m1*V(i,j) + m2*V(i,3+j) + m3*V(i,6+j))/(m1+m2+m3);

250 end %Joint Positions JOINT(i,1:3) = (s(i,1:3)'- RT2*[0 0 l2/2]')'; JOINT(i,4:6) = (s(i,1:3)'+ RT2*[0 0 l2/2]')'; end

Generalized Coordinate Accelerations – TT.m %This function computes the accelerations of the generalized coordinates %Format -> %A = [xtt,ytt,ztt,ptt1,qtt1,wtt1,ptt2,qtt2,wtt2,ptt3,qtt3,wtt3] function [A] = TT (s) %Read Constants Constants; %Read the Torques Ts; %Size of s [m n] = size(s); %Initialize A A = zeros(m,12); %Loop for all points for i=1:m %Compute the Coefficients - Csi.m Csi; %Compute the 2nd Derivatives - Needed for Rate of Change of Momentum A(i,1) = C1 * (C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54

251 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25) + C2 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C3 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C4 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C5 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C6 * (C52 * C54 + C53) + C7; A(i,2) = C8 * (C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52

252 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25) + C9 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C10 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C11 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C12 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C13 * (C52 * C54 + C53) + C14; A(i,3) = C15 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) +

253 C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C16 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C17 * (C52 * C54 + C53) + C18; A(i,4) = C19 * (C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31) + C20 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C21 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C22 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C23 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C24 * (C52 * C54 + C53) + C25; A(i,5) = C26 * (C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 *

254 C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36) + C27 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C28 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C29 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C30 * (C52 * C54 + C53) + C31; A(i,6) = C32 * (C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41) + C33 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C34 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C35 * (C52 * C54 + C53) + C36; A(i,7) = C37 * (C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45) + C38 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C39 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C40 * (C52 * C54 + C53) + C41; A(i,8) = C42 * (C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48) + C43 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C44 * (C52 * C54 + C53) + C45; A(i,9) = C46 * (C49 * (C52 * C54 + C53) + C50 * C54 + C51) + C47 * (C52 * C54 + C53) + C48; A(i,10) = C49 * (C52 * C54 + C53) + C50 * C54 + C51; A(i,11) = C52 * C54 + C53; A(i,12) = C54; end

Body Axis Angular Velocities – Omega.m %This function returns the vector form of the body axis angular velocities %Format

w = [wx,wy,wz]

function [w1, w2, w3] = Omega (s) %Size of s [m n] = size(s);

255 %Initialize Variables w1 = zeros(m,3); w2 = zeros(m,3); w3 = zeros(m,3); %Loop for all s for i=1:m %Angular Velocity Definitions w1(i,:) = [s(i,16) * sin(s(i,5)) * sin(s(i,6)) + s(i,17) * cos(s(i,6)) s(i,16) * sin(s(i,5)) * cos(s(i,6)) - s(i,17) * sin(s(i,6)) s(i,16) * cos(s(i,5)) + s(i,18)]; w2(i,:) = [s(i,19) * sin(s(i,8)) * sin(s(i,9)) + s(i,20) * cos(s(i,9)) s(i,19) * sin(s(i,8)) * cos(s(i,9)) - s(i,20) * sin(s(i,9)) s(i,19) * cos(s(i,8)) + s(i,21)]; w3(i,:) = [s(i,22) * sin(s(i,11)) * sin(s(i,12)) + s(i,23) * cos(s(i,12)) s(i,22) * sin(s(i,11)) * cos(s(i,12)) - s(i,23) * sin(s(i,12)) s(i,22) * cos(s(i,11)) + s(i,24)]; end

Control Effort, Cross Products, & Joint Angles – Controls.m %This function calculates the control effort, actual cross product values, and the inverse dot product joint angle. %Formats: %

JA1 = [JA1], JA2 = [JA2], CR1,CR2 = [X,Y,Z] T1, T3 = [X,Y,Z]

function [JA1,JA2, CR1, CR2, T1, T3] = Controls (s) %Read Constants Constants; % Size of s - Need this for the Loop [m n] = size(s); %Initialize the variables JA1 = zeros(m,1); JA2 = zeros(m,1); CR1 = zeros(m,3); CR2 = zeros(m,3); T1 = zeros(m,3); T3 = zeros(m,3); %Loop for all rows in s for i=1:m %Calculate the rotation matrices for this time step - Rotations.m

256 [R1, RT1, Rdot1, RTdot1, R2, RT2, Rdot2, RTdot2, R3, RT3, Rdot3, RTdot3] = Rotations (s, i); %Z z1 z2 z3

body axes rotated to spatial frame = RT1*[0 0 1]'; = RT2*[0 0 1]'; = RT3*[0 0 1]';

%Dot products between adjoining links JA1(i,1) = acosd ( (z1'*z2)/(sqrt(z1'*z1)*sqrt(z2'*z2))); JA2(i,1) = acosd ( (z2'*z3)/(sqrt(z3'*z3)*sqrt(z2'*z2))); %Cross products between adjoining links CR1(i,:) = CROSS(z1,z2); CR2(i,:) = CROSS(z2,z3); %Torque Magnitudes and Control Effort T1(i,:) = [KZ1 * (-sin(s(i,5)) * cos(s(i,4)) * cos(s(i,8)) + cos(s(i,5)) * sin(s(i,8)) * cos(s(i,7)) - d11) + JZ1 * (sin(s(i,5)) * sin(s(i,4)) * cos(s(i,8)) * s(i,16) - s(i,17) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,8)) - s(i,17) * sin(s(i,5)) * sin(s(i,8)) * cos(s(i,7)) - cos(s(i,5)) * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + s(i,20) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,8)) + s(i,20) * cos(s(i,5)) * cos(s(i,8)) * cos(s(i,7))) + KX1 * ((cos(s(i,6)) * sin(s(i,4)) + sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * sin(s(i,9)) * sin(s(i,8)) - sin(s(i,6)) * sin(s(i,5)) * (cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)))) + JX1 * (sin(s(i,9)) * sin(s(i,8)) * s(i,16) * cos(s(i,6)) * cos(s(i,4)) - sin(s(i,9)) * sin(s(i,8)) * s(i,16) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) s(i,17) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * sin(s(i,8)) - s(i,17) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,9)) * sin(s(i,7)) - s(i,17) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * sin(s(i,4)) + s(i,18) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) - s(i,18) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * sin(s(i,7)) - s(i,18) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - sin(s(i,6)) * sin(s(i,5)) * s(i,19) * cos(s(i,9)) * cos(s(i,7)) + sin(s(i,6)) * sin(s(i,5)) * s(i,19) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,20) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,6)) * sin(s(i,4)) + s(i,20) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,20) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) + s(i,21) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * sin(s(i,4)) + s(i,21) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,21) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * sin(s(i,7)) - s(i,21) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) + KY1 * ((sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * cos(s(i,9)) * sin(s(i,8)) - cos(s(i,6)) * sin(s(i,5)) * (-sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)))) + JY1 * (cos(s(i,9)) * sin(s(i,8)) * s(i,16) * sin(s(i,6)) * cos(s(i,4)) cos(s(i,9)) * sin(s(i,8)) * s(i,16) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) - s(i,17) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * sin(s(i,8)) + s(i,17) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,9)) * sin(s(i,7)) - s(i,17) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * cos(s(i,9)) *

257 sin(s(i,8)) * cos(s(i,6)) * sin(s(i,4)) - s(i,18) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) - s(i,18) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * sin(s(i,7)) + s(i,18) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + cos(s(i,6)) * sin(s(i,5)) * s(i,19) * sin(s(i,9)) * cos(s(i,7)) + cos(s(i,6)) * sin(s(i,5)) * s(i,19) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,20) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,6)) * sin(s(i,4)) + s(i,20) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,20) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) + s(i,21) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * sin(s(i,4)) - s(i,21) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,21) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * sin(s(i,7)) + s(i,21) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) KZ1 * (cos(s(i,5)) * sin(s(i,8)) * sin(s(i,7)) - sin(s(i,5)) * sin(s(i,4)) * cos(s(i,8)) - d12) + JZ1 * (-sin(s(i,5)) * cos(s(i,4)) * cos(s(i,8)) * s(i,16) - s(i,17) * sin(s(i,5)) * sin(s(i,8)) * sin(s(i,7)) - s(i,17) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,8)) + cos(s(i,5)) * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + s(i,20) * cos(s(i,5)) * cos(s(i,8)) * sin(s(i,7)) + s(i,20) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,8))) + KX1 * (sin(s(i,6)) * sin(s(i,5)) * (cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) (cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * sin(s(i,9)) * sin(s(i,8))) + JX1 * (sin(s(i,9)) * sin(s(i,8)) * s(i,16) * cos(s(i,6)) * sin(s(i,4)) + sin(s(i,9)) * sin(s(i,8)) * s(i,16) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,17) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,9)) * cos(s(i,7)) - s(i,17) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,17) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,8)) + s(i,18) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,7)) s(i,18) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,18) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,4)) + s(i,18) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) - sin(s(i,6)) * sin(s(i,5)) * s(i,19) * cos(s(i,9)) * sin(s(i,7)) - sin(s(i,6)) * sin(s(i,5)) * s(i,19) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,20) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) - s(i,20) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,6)) * cos(s(i,4)) + s(i,20) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) s(i,21) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,7)) s(i,21) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,21) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,4)) + s(i,21) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) + KY1 * (cos(s(i,6)) * sin(s(i,5)) * (sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) (-sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * cos(s(i,9)) * sin(s(i,8))) + JY1 * (-cos(s(i,9)) * sin(s(i,8)) * s(i,16) * sin(s(i,6)) * sin(s(i,4)) + cos(s(i,9)) * sin(s(i,8)) * s(i,16) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) - s(i,17) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,9)) * cos(s(i,7)) - s(i,17) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) s(i,17) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,8)) + s(i,18) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,7)) + s(i,18) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,18) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,4)) - s(i,18) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) + cos(s(i,6)) * sin(s(i,5)) *

258 s(i,19) * sin(s(i,9)) * sin(s(i,7)) - cos(s(i,6)) * sin(s(i,5)) * s(i,19) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,20) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) + s(i,20) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,6)) * cos(s(i,4)) + s(i,20) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) - s(i,21) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,9)) * cos(s(i,7)) + s(i,21) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,21) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,6)) * cos(s(i,4)) - s(i,21) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) KZ1 * (-sin(s(i,5)) * sin(s(i,4)) * sin(s(i,8)) * cos(s(i,7)) + sin(s(i,5)) * cos(s(i,4)) * sin(s(i,8)) * sin(s(i,7)) - d13) + JZ1 * (-s(i,16) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,8)) * cos(s(i,7)) - s(i,16) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,8)) * sin(s(i,7)) - s(i,17) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,8)) * cos(s(i,7)) + s(i,17) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,8)) * sin(s(i,7)) + s(i,19) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,8)) * sin(s(i,7)) + s(i,19) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,8)) * cos(s(i,7)) - s(i,20) * sin(s(i,5)) * sin(s(i,4)) * cos(s(i,8)) * cos(s(i,7)) + s(i,20) * sin(s(i,5)) * cos(s(i,4)) * cos(s(i,8)) * sin(s(i,7))) + KX1 * ((cos(s(i,6)) * cos(s(i,4)) - sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * (cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) - (cos(s(i,6)) * sin(s(i,4)) + sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * (cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)))) + JX1 * (s(i,17) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,18) * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) - s(i,18) * sin(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) - s(i,18) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,18) * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) - s(i,16) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * sin(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,18) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) + s(i,18) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,19) * cos(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) + s(i,16) * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,19) * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,19) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) + s(i,19) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,19) * cos(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) + s(i,19) * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,19) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) + s(i,16) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) + s(i,19) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,16) * cos(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) - s(i,20) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,6)) * cos(s(i,4)) - s(i,20) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,6)) * sin(s(i,4)) + s(i,20) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) - s(i,20) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) - s(i,21) * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,21) * cos(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,21) *

259 sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) s(i,16) * cos(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) s(i,21) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,21) * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) + s(i,21) * cos(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,21) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) + s(i,21) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,17) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) - s(i,16) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,17) * sin(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,17) * sin(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) - s(i,16) * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,16) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * sin(s(i,7))) + KY1 * ((sin(s(i,6)) * cos(s(i,4)) - cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4))) * (-sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) - (-sin(s(i,6)) * sin(s(i,4)) + cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4))) * (-sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)))) + JY1 * (-s(i,17) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) - s(i,17) * cos(s(i,6)) * sin(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) s(i,18) * cos(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,18) * sin(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,18) * cos(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,19) * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,18) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) - s(i,18) * sin(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,19) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) + s(i,19) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,19) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,19) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) s(i,19) * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,17) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,19) * sin(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,19) * sin(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) + s(i,20) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,6)) * cos(s(i,4)) + s(i,20) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,6)) * sin(s(i,4)) + s(i,20) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) - s(i,18) * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) - s(i,20) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) + s(i,21) * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) + s(i,21) * sin(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,21) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * sin(s(i,7)) + s(i,21) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,21) * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) + s(i,21) * sin(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,21) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,7)) - s(i,21) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,8)) *

260 sin(s(i,7)) - s(i,16) * sin(s(i,6)) * sin(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) + s(i,17) * cos(s(i,6)) * sin(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,16) * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,16) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,9)) * sin(s(i,7)) s(i,16) * cos(s(i,6)) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,16) * sin(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) - s(i,16) * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,16) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,9)) * cos(s(i,7)) - s(i,16) * cos(s(i,6)) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,18) * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,9)) * sin(s(i,7)))]; T3(i,:) = [KZ3 * (-sin(s(i,8)) * cos(s(i,7)) * cos(s(i,11)) + cos(s(i,8)) * sin(s(i,11)) * cos(s(i,10)) - d31) + JZ3 * (sin(s(i,8)) * sin(s(i,7)) * cos(s(i,11)) * s(i,19) - s(i,20) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,11)) - s(i,20) * sin(s(i,8)) * sin(s(i,11)) * cos(s(i,10)) - cos(s(i,8)) * sin(s(i,11)) * sin(s(i,10)) * s(i,22) + s(i,23) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,11)) + s(i,23) * cos(s(i,8)) * cos(s(i,11)) * cos(s(i,10))) + KX3 * ((cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * sin(s(i,12)) * sin(s(i,11)) - sin(s(i,9)) * sin(s(i,8)) * (cos(s(i,12)) * sin(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)))) + JX3 * (sin(s(i,12)) * sin(s(i,11)) * s(i,19) * cos(s(i,9)) * cos(s(i,7)) - sin(s(i,12)) * sin(s(i,11)) * s(i,19) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) s(i,20) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * sin(s(i,11)) - s(i,20) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,12)) * sin(s(i,10)) - s(i,20) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,21) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * sin(s(i,7)) + s(i,21) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,21) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * sin(s(i,10)) - s(i,21) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - sin(s(i,9)) * sin(s(i,8)) * s(i,22) * cos(s(i,12)) * cos(s(i,10)) + sin(s(i,9)) * sin(s(i,8)) * s(i,22) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,23) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,9)) * sin(s(i,7)) + s(i,23) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,23) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) + s(i,24) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * sin(s(i,7)) + s(i,24) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,24) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * sin(s(i,10)) - s(i,24) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) + KY3 * ((sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * cos(s(i,12)) * sin(s(i,11)) - cos(s(i,9)) * sin(s(i,8)) * (sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)))) + JY3 * (-cos(s(i,12)) * sin(s(i,11)) * s(i,19) * sin(s(i,9)) * cos(s(i,7)) - cos(s(i,12)) * sin(s(i,11)) * s(i,19) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,20) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * sin(s(i,11)) + s(i,20) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,12)) * sin(s(i,10)) - s(i,20) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,21) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * sin(s(i,7)) s(i,21) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) - s(i,21) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * sin(s(i,10)) + s(i,21) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + cos(s(i,9)) * sin(s(i,8)) * s(i,22) *

261 sin(s(i,12)) * cos(s(i,10)) + cos(s(i,9)) * sin(s(i,8)) * s(i,22) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,23) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,9)) * sin(s(i,7)) + s(i,23) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,23) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) + s(i,24) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * sin(s(i,7)) s(i,24) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,24) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * sin(s(i,10)) + s(i,24) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) KZ3 * (cos(s(i,8)) * sin(s(i,11)) * sin(s(i,10)) - sin(s(i,8)) * sin(s(i,7)) * cos(s(i,11)) - d32) + JZ3 * (-sin(s(i,8)) * cos(s(i,7)) * cos(s(i,11)) * s(i,19) - s(i,20) * sin(s(i,8)) * sin(s(i,11)) * sin(s(i,10)) - s(i,20) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,11)) + cos(s(i,8)) * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + s(i,23) * cos(s(i,8)) * cos(s(i,11)) * sin(s(i,10)) + s(i,23) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,11))) + KX3 * (sin(s(i,9)) * sin(s(i,8)) * (cos(s(i,12)) * cos(s(i,10)) sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) - (cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * sin(s(i,12)) * sin(s(i,11))) + JX3 * (sin(s(i,12)) * sin(s(i,11)) * s(i,19) * cos(s(i,9)) * sin(s(i,7)) + sin(s(i,12)) * sin(s(i,11)) * s(i,19) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,20) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,12)) * cos(s(i,10)) - s(i,20) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,20) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,11)) + s(i,21) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,10)) s(i,21) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,21) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,7)) + s(i,21) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - sin(s(i,9)) * sin(s(i,8)) * s(i,22) * cos(s(i,12)) * sin(s(i,10)) - sin(s(i,9)) * sin(s(i,8)) * s(i,22) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,23) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) - s(i,23) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,9)) * cos(s(i,7)) + s(i,23) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) s(i,24) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,10)) s(i,24) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,24) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,7)) + s(i,24) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) + KY3 * (cos(s(i,9)) * sin(s(i,8)) * (sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) - (-sin(s(i,9)) * cos(s(i,7)) - cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * cos(s(i,12)) * sin(s(i,11))) + JY3 * (-cos(s(i,12)) * sin(s(i,11)) * s(i,19) * sin(s(i,9)) * sin(s(i,7)) + cos(s(i,12)) * sin(s(i,11)) * s(i,19) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) s(i,20) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,12)) * cos(s(i,10)) s(i,20) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,20) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,11)) + s(i,21) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,10)) + s(i,21) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,21) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,7)) - s(i,21) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + cos(s(i,9)) * sin(s(i,8)) * s(i,22) * sin(s(i,12)) * sin(s(i,10)) - cos(s(i,9)) * sin(s(i,8)) * s(i,22) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,23) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) + s(i,23) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,9)) *

262 cos(s(i,7)) + s(i,23) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) - s(i,24) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,12)) * cos(s(i,10)) + s(i,24) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,24) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,9)) * cos(s(i,7)) - s(i,24) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) KZ3 * (sin(s(i,8)) * sin(s(i,7)) * sin(s(i,11)) * cos(s(i,10)) + sin(s(i,8)) * cos(s(i,7)) * sin(s(i,11)) * sin(s(i,10)) - d33) + JZ3 * (-s(i,19) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,11)) * cos(s(i,10)) - s(i,19) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,11)) * sin(s(i,10)) - s(i,20) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,11)) * cos(s(i,10)) + s(i,20) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,11)) * sin(s(i,10)) + s(i,22) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,11)) * sin(s(i,10)) + s(i,22) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,11)) * cos(s(i,10)) - s(i,23) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,11)) * cos(s(i,10)) + s(i,23) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,11)) * sin(s(i,10))) + KX3 * ((cos(s(i,9)) * cos(s(i,7)) - sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * (cos(s(i,12)) * sin(s(i,10)) + sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) - (cos(s(i,9)) * sin(s(i,7)) + sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * (cos(s(i,12)) * cos(s(i,10)) - sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)))) + JX3 * (-s(i,24) * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,24) * cos(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) - s(i,19) * cos(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) - s(i,19) * cos(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) - s(i,21) * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,22) * cos(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,22) * cos(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) + s(i,21) * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) - s(i,23) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,23) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) + s(i,24) * cos(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,24) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,24) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) - s(i,24) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,22) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,24) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) s(i,23) * sin(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * cos(s(i,9)) * sin(s(i,7)) - s(i,23) * sin(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * cos(s(i,9)) * cos(s(i,7)) + s(i,22) * cos(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,24) * cos(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,19) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) s(i,19) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,19) * cos(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,19) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,20) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,20) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) + s(i,19) * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,22) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,19) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,22) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * cos(s(i,9)) *

263 cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) - s(i,22) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) + s(i,21) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * sin(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,22) * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,20) * sin(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,21) * sin(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,20) * sin(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10))) + KY3 * ((-sin(s(i,9)) * cos(s(i,7)) cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7))) * (-sin(s(i,12)) * sin(s(i,10)) + cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10))) - (sin(s(i,9)) * sin(s(i,7)) + cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7))) * (-sin(s(i,12)) * cos(s(i,10)) - cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)))) + JY3 * (-s(i,19) * sin(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,21) * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) - s(i,19) * sin(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) + s(i,24) * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,22) * sin(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,22) * sin(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) - s(i,21) * cos(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) - s(i,24) * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) + s(i,23) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * sin(s(i,9)) * sin(s(i,7)) + s(i,19) * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,19) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) s(i,19) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,19) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) - s(i,19) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,19) * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,20) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,20) * cos(s(i,9)) * sin(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,20) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) s(i,20) * cos(s(i,9)) * sin(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * cos(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,21) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,21) * sin(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,21) * cos(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,21) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) - s(i,21) * sin(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) - s(i,22) * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) - s(i,23) * cos(s(i,12)) * sin(s(i,11)) * sin(s(i,10)) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) + s(i,22) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,10)) + s(i,22) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,22) * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,24) * sin(s(i,9)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,23) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * sin(s(i,9)) * cos(s(i,7)) + s(i,23) * cos(s(i,12)) * sin(s(i,11)) * cos(s(i,10)) * cos(s(i,9)) * cos(s(i,8))

264 * sin(s(i,7)) - s(i,22) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * sin(s(i,10)) + s(i,22) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,24) * sin(s(i,9)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)) + s(i,24) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,12)) * sin(s(i,10)) + s(i,24) * cos(s(i,9)) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * cos(s(i,10)) + s(i,24) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,12)) * cos(s(i,10)) - s(i,24) * cos(s(i,9)) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,12)) * cos(s(i,11)) * sin(s(i,10)))]; end

Linear & Angular Momentum Calculations – Momentum.m %This function calculates and returns the linear and angular momentum of the system. %Variable Format % Linear momentum -> P = [Px, Py, Pz] % Angular Momentum WRT to the Origin -> L = [Lx,Ly,Lz] % Rate of Change of the Angular Momentum WRT to the Origin -> Ldot = [Ldotx,Ldoty,Ldotz] % Torque on the body WRT to the Origin -> T = [Tx,Ty,Tz] function [P, L, T, Ldot] = Momentum(s,A) %Read Constants Constants; %Size of s [m n] = size (s); %Initialize variables P = zeros (m,3); LO = zeros(m,3); T = zeros(m,3); LOdot = zeros(m,3); %Loop for all of s for i=1:m %Rotations [R1, RT1, Rdot1, RTdot1, R2, RT2, Rdot2, RTdot2, R3, RT3, Rdot3, RTdot3] = Rotations (s, i);

%Linear Momentum P(i,:) = [(8 * m1 * s(i,13)) - 0.4e1 * m1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) - 0.4e1 * m1 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) - 0.4e1 * m1 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) - 0.4e1

265 * m1 * l1 * cos(s(i,5)) * sin(s(i,4)) * s(i,17) + (8 * m2 * s(i,13)) + (8 * m3 * s(i,13)) + 0.4e1 * m3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m3 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.4e1 * m3 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + 0.4e1 * m3 * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,23) (8 * m1 * s(i,14)) - 0.4e1 * m1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + 0.4e1 * m1 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.4e1 * m1 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) + 0.4e1 * m1 * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,17) + (8 * m2 * s(i,14)) + (8 * m3 * s(i,14)) + 0.4e1 * m3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.4e1 * m3 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) + 0.4e1 * m3 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) - 0.4e1 * m3 * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,23) (8 * m1 * s(i,15)) + 0.4e1 * m1 * sin(s(i,8)) * s(i,20) * l2 + 0.4e1 * m1 * sin(s(i,5)) * s(i,17) * l1 + (8 * m2 * s(i,15)) + (8 * m3 * s(i,15)) 0.4e1 * m3 * sin(s(i,8)) * s(i,20) * l2 - 0.4e1 * m3 * sin(s(i,11)) * s(i,23) * l3]; %Angular Momentum about the origin L(i,:) = [0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) + 0.4e1 * m1 * s(i,2) * sin(s(i,8)) * s(i,20) * l2 + 0.4e1 * m1 * s(i,2) * sin(s(i,5)) * s(i,17) * l1 + 0.4e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * s(i,15) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * sin(s(i,5)) * s(i,17) * l1 + 0.8e1 * m3 * s(i,2) * s(i,15) - 0.8e1 * m3 * s(i,3) * s(i,14) + 0.4e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * s(i,15) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * sin(s(i,8)) * s(i,20) * l2 - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) - 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,12)) * sin(s(i,10)) * cos(s(i,12)) * cos(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,9)) * cos(s(i,7)) + 0.8e1 * m1 * s(i,2) * s(i,15) + 0.8e1 * s(i,2) * m2 * s(i,15) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,6)) * cos(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * sin(s(i,12)) * cos(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,10)) - 0.4e1 * m3 * cos(s(i,11)) * l3 * s(i,14) + 0.4e1 * m1 * cos(s(i,5)) * l1 * s(i,14) - 0.4e1 * m3 * cos(s(i,8)) * l2 * s(i,14) - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + 0.4e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) - 0.4e1 * m3 * s(i,2) * sin(s(i,8)) * s(i,20) * l2 + 0.4e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,23) - 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) - 0.8e1 * s(i,3) * m2 * s(i,14) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * s(i,23) + 0.2e1 * m3 * cos(s(i,7)) * l2 ^ 2 * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,24) * sin(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * sin(s(i,4)) - 0.4e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,17) - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,7)) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,9)) ^ 2 + 0.4e1 * m1 * cos(s(i,8)) * l2 * s(i,14) + 0.2e1 / 0.3e1 * cos(s(i,7)) * l2 ^ 2 * m2 * s(i,20) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * s(i,20) + 0.2e1 * m1 * cos(s(i,7)) * l2 ^ 2 * s(i,20) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 *

266 cos(s(i,4)) * s(i,17) + 0.8e1 / 0.3e1 * cos(s(i,4)) * l1 ^ 2 * m1 * s(i,17) + 0.8e1 / 0.3e1 * cos(s(i,10)) * l3 ^ 2 * m3 * s(i,23) - 0.4e1 * m3 * s(i,2) * sin(s(i,11)) * s(i,23) * l3 - 0.4e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * s(i,15) + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * sin(s(i,11)) * s(i,23) * l3 + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * cos(s(i,4)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * s(i,17) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,18) * sin(s(i,4)) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,10)) * sin(s(i,11)) * s(i,24) - 0.8e1 * m1 * s(i,3) * s(i,14) + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,23) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,4)) * sin(s(i,5)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * cos(s(i,10)) * s(i,23) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,7)) * sin(s(i,8)) * s(i,21) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,21) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * cos(s(i,7)) * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,10)) - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,10)) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * s(i,23) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * s(i,20) * cos(s(i,9)) ^ 2 - 0.4e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * s(i,15) + 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * sin(s(i,6)) * cos(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * sin(s(i,4)) + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.4e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) - 0.2e1 * m1 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,17) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * sin(s(i,8)) * s(i,20) * l2 - 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,12)) * cos(s(i,10)) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,12)) * sin(s(i,10)) * cos(s(i,12)) * cos(s(i,11)) * s(i,23) + 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.8e1 / 0.3e1 * m1 * cos(s(i,5)) * l1 ^ 2 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) * sin(s(i,4)) * cos(s(i,6)) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,6)) * cos(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * sin(s(i,9)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,7)) -0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * cos(s(i,10)) + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,23) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * sin(s(i,9)) * sin(s(i,7)) + 0.2e1 * m1 * sin(s(i,7)) * l2 ^ 2 * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,4)) * l1 ^ 2 * m1 * s(i,17) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * s(i,17) + 0.4e1 * m3 * cos(s(i,8)) * l2 * s(i,13) + 0.4e1 * m3 * cos(s(i,11)) * l3 * s(i,13) - 0.4e1 * m1 *

267 cos(s(i,8)) * l2 * s(i,13) - 0.4e1 * m1 * cos(s(i,5)) * l1 * s(i,13) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * s(i,20) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,12)) * cos(s(i,10)) * cos(s(i,12)) * cos(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,12)) * sin(s(i,10)) - 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,6)) * sin(s(i,4)) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,12)) * cos(s(i,10)) * cos(s(i,12)) * cos(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * s(i,23) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,9)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * cos(s(i,4)) + 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * sin(s(i,10)) * s(i,23) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * s(i,17) * cos(s(i,6)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * cos(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * cos(s(i,10)) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,10)) * sin(s(i,11)) * s(i,24) - 0.4e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * s(i,23) * cos(s(i,12)) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * sin(s(i,4)) * s(i,17) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * s(i,20) * cos(s(i,9)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,24) * cos(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * sin(s(i,7)) * s(i,20) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,7)) * sin(s(i,8)) * s(i,21) + 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + 0.4e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,23) + 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.8e1 / 0.3e1 * cos(s(i,5)) * l1 ^ 2 * m1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) + 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + 0.8e1 / 0.3e1 * sin(s(i,10)) * l3 ^ 2 * m3 * s(i,23) - 0.4e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * s(i,15) + 0.4e1 * m3 * s(i,1) * sin(s(i,11)) * s(i,23) * l3 - 0.4e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * s(i,15) - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,18) * cos(s(i,4)) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,4)) * sin(s(i,5)) * s(i,18) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,21) * cos(s(i,7)) - 0.8e1 * m1 * s(i,1) * s(i,15) - 0.8e1 * s(i,1) * m2 * s(i,15) + 0.2e1 * m1 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * s(i,15) 0.4e1 * m1 * s(i,1) * sin(s(i,5)) * s(i,17) * l1 - 0.4e1 * m1 * s(i,1) * sin(s(i,8)) * s(i,20) * l2 + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,6)) ^ 2 - 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) - 0.4e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * sin(s(i,4)) * s(i,17) + 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m3 * s(i,1) * sin(s(i,8)) * s(i,20) * l2 - 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * s(i,15) + 0.8e1 * m1 * s(i,3) * s(i,13) + 0.8e1 * s(i,3) * m2 * s(i,13) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * sin(s(i,8)) * s(i,20) * l2 + 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * sin(s(i,6)) * sin(s(i,4)) + 0.2e1 / 0.3e1 * sin(s(i,7)) * l2 ^ 2 * m2 * s(i,20) + 0.8e1 * m3 * s(i,3) * s(i,13) + 0.2e1 * m1 * cos(s(i,5)) * l1

268 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * cos(s(i,4)) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,6)) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * sin(s(i,12)) * sin(s(i,10)) + 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * s(i,17) - 0.8e1 * m3 * s(i,1) * s(i,15) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * sin(s(i,5)) * s(i,17) * l1 - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * cos(s(i,4)) * sin(s(i,6)) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,9)) * sin(s(i,7)) + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.2e1 * m3 * sin(s(i,7)) * l2 ^ 2 * s(i,20) + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * sin(s(i,11)) * s(i,23) * l3 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * sin(s(i,8)) * s(i,20) * l2 + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) 0.8e1 * m1 * s(i,1) * s(i,14) - 0.8e1 * m3 * s(i,2) * s(i,13) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * s(i,16) + 0.2e1 * m1 * l2 ^ 2 * s(i,19) + 0.2e1 * m3 * l2 ^ 2 * s(i,19) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * s(i,22) + 0.8e1 * s(i,1) * m2 * s(i,14) + 0.8e1 / 0.3e1 * l1 ^ 2 * m1 * s(i,16) - 0.8e1 * m1 * s(i,2) * s(i,13) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) ^ 2 * s(i,19) + 0.8e1 * m3 * s(i,1) * s(i,14) - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,23) + 0.4e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * s(i,14) + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.4e1 * m3 * s(i,2) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) - 0.4e1 * m3 * s(i,2) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.4e1 * m1 * s(i,1) * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.4e1 * m1 * s(i,1) * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) + 0.4e1 * m1 * s(i,1) * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,17) - 0.4e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * s(i,14) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) + 0.4e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * s(i,13) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) ^ 2 * s(i,16) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * sin(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * sin(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) ^ 2 * s(i,16) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) * sin(s(i,9)) * sin(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) ^ 2 * s(i,19) * cos(s(i,9)) ^ 2 + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * cos(s(i,8)) ^ 2 * s(i,19) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * s(i,19) * cos(s(i,9)) ^ 2 - 0.8e1 / 0.3e1 * l1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) ^ 2 + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * s(i,16) - 0.8e1 / 0.3e1 * l3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) ^ 2 - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * s(i,22) * cos(s(i,12)) ^ 2 - 0.2e1 * m3 * l2 ^ 2 * s(i,19) * cos(s(i,8)) ^ 2 - 0.2e1 * m1 * l2 ^ 2 * s(i,19) * cos(s(i,8)) ^ 2 + 0.2e1 / 0.3e1 * l2 ^ 2 * m2 * s(i,19) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,8)) * s(i,21) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * s(i,22) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) ^ 2 * s(i,22) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) * s(i,18) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * s(i,16) * cos(s(i,6)) ^ 2 - 0.2e1 / 0.3e1 * l2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) ^ 2 + 0.8e1 / 0.3e1 * l3 ^ 2 * m3 * s(i,22) -

269 0.4e1 * m3 * s(i,2) * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) 0.4e1 * m3 * s(i,2) * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,23) + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,23) + 0.4e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * s(i,13) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * cos(s(i,11)) ^ 2 * s(i,22) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * s(i,17) - 0.4e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * s(i,13) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.4e1 * m3 * s(i,1) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.4e1 * m3 * s(i,1) * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) + 0.4e1 * m3 * s(i,1) * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) - 0.4e1 * m3 * s(i,1) * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,23) + 0.4e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * s(i,14) + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * s(i,19) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,5)) * s(i,18) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * s(i,19) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) * s(i,24) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) * s(i,21) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,11)) * s(i,24) - 0.8e1 * s(i,2) * m2 * s(i,13) + 0.4e1 * m1 * s(i,2) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) + 0.4e1 * m1 * s(i,2) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,20) + 0.4e1 * m1 * s(i,2) * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) - 0.4e1 * m1 * s(i,1) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) + 0.4e1 * m1 * s(i,2) * l1 * cos(s(i,5)) * sin(s(i,4)) * s(i,17) - 0.4e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * s(i,13) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) ^ 2 * s(i,22) * cos(s(i,12)) ^ 2 - 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,17) - 0.4e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * s(i,14) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) - 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,20) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) * sin(s(i,9)) * sin(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * cos(s(i,5)) ^ 2 * s(i,16)]; %Rate of Change of the Angular momentum about the origin Ldot(i,:) = [-0.2e1 / 0.3e1 * sin(s(i,7)) * s(i,19) * l2 ^ 2 * m2 * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,6)) * sin(s(i,4)) + 0.4e1 * m1 * s(i,2) * cos(s(i,5)) * s(i,17) ^ 2 * l1 - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * sin(s(i,4)) * s(i,16) * s(i,17) - 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * sin(s(i,10)) * A(i,10) + 0.8e1 / 0.3e1 * m3 * sin(s(i,11)) ^ 2 * s(i,23) * l3 ^ 2 * sin(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) ^ 2 * l3 ^ 2 * s(i,23) * sin(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * A(i,8) + 0.4e1 * m1 * s(i,2) * sin(s(i,5)) * A(i,5) * l1 - 0.8e1 / 0.3e1 * cos(s(i,11)) ^ 2 * s(i,23) * a3 ^ 2 * m3 * s(i,22) * sin(s(i,10)) *

270 cos(s(i,12)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,11)) ^ 2 * a3 ^ 2 * m3 * s(i,22) * s(i,23) * sin(s(i,10)) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * cos(s(i,10)) * cos(s(i,12)) ^ 2 + 0.16e2 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,10)) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,9) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,8)) * s(i,20) * a2 ^ 2 * m2 * s(i,21) * sin(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,21) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,4)) * sin(s(i,5)) * A(i,6) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,4)) * s(i,16) * sin(s(i,5)) * s(i,18) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,4)) * cos(s(i,5)) * s(i,17) * s(i,18) - 0.2e1 * m1 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.2e1 * m1 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * sin(s(i,7)) * s(i,19) - 0.2e1 * m1 * cos(s(i,8)) ^ 2 * l2 ^ 2 * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 * m1 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * A(i,4) - 0.4e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) - 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * A(i,5) 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,9)) ^ 2 - 0.8e1 / 0.3e1 * cos(s(i,8)) ^ 2 * s(i,20) * a2 ^ 2 * m2 * s(i,19) * sin(s(i,7)) * cos(s(i,9)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,8)) ^ 2 * a2 ^ 2 * m2 * s(i,19) * s(i,20) * sin(s(i,7)) * cos(s(i,9)) ^ 2 + 0.16e2 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) - 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) ^ 2 * sin(s(i,9)) * sin(s(i,7)) 0.4e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * cos(s(i,4)) * A(i,5) + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - 0.4e1 * m3 * cos(s(i,11)) * l3 * A(i,2) - 0.4e1 * m3 * cos(s(i,8)) * l2 * A(i,2) + 0.8e1 / 0.3e1 * cos(s(i,10)) * l3 ^ 2 * m3 * A(i,11) + 0.2e1 / 0.3e1 * cos(s(i,7)) * l2 ^ 2 * m2 * A(i,8) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * A(i,8) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * A(i,5) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * A(i,11) + 0.2e1 * m3 * cos(s(i,7)) * l2 ^ 2 * A(i,8) + 0.8e1 / 0.3e1 * cos(s(i,4)) * l1 ^ 2 * m1 * A(i,5) + 0.2e1 * m1 * cos(s(i,7)) * l2 ^ 2 * A(i,8) + 0.4e1 * m1 * cos(s(i,8)) * l2 * A(i,2) + 0.4e1 * m1 * cos(s(i,5)) * l1 * A(i,2) - 0.8e1 * s(i,3) * m2 * A(i,2) + 0.8e1 * m3 * s(i,2) * A(i,3) - 0.8e1 * m3 * s(i,3) * A(i,2) + 0.8e1 * s(i,2) * m2 * A(i,3) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * sin(s(i,4)) * s(i,18) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,6)) * sin(s(i,5)) * s(i,17) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,6)) * cos(s(i,4)) + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * sin(s(i,11)) * A(i,11) * l3 + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * cos(s(i,11)) * s(i,23) ^ 2 * l3 - 0.4e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * A(i,3) - 0.8e1 / 0.3e1 * m1 * cos(s(i,5)) ^ 2 * l1 ^ 2 * s(i,17) * sin(s(i,4)) * s(i,16) - 0.8e1 / 0.3e1 * m1 * cos(s(i,5)) * l1 ^ 2 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 - 0.4e1 * m3 * s(i,2) * sin(s(i,11)) * A(i,11) * l3 - 0.4e1 * m3 * s(i,2) * cos(s(i,11)) * s(i,23) ^ 2 * l3 0.4e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * A(i,3) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * sin(s(i,7)) * s(i,21) * cos(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) *

271 cos(s(i,9)) * sin(s(i,8)) * s(i,20) ^ 2 + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,10)) * sin(s(i,12)) * cos(s(i,11)) * A(i,11) 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,10)) * cos(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * sin(s(i,10)) * s(i,24) * cos(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,10)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) ^ 2 - 0.8e1 / 0.3e1 * cos(s(i,5)) ^ 2 * s(i,17) * a1 ^ 2 * m1 * s(i,16) * sin(s(i,4)) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,5)) ^ 2 * a1 ^ 2 * m1 * s(i,16) * s(i,17) * sin(s(i,4)) * cos(s(i,6)) ^ 2 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,6)) ^ 2 + 0.16e2 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,6)) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * sin(s(i,7)) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * s(i,22) * s(i,23) + 0.8e1 / 0.3e1 * cos(s(i,8)) ^ 2 * s(i,20) * a2 ^ 2 * m2 * s(i,19) * sin(s(i,7)) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,7)) * cos(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * sin(s(i,7)) * s(i,21) * cos(s(i,8)) * s(i,20) + 0.2e1 * m3 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,8)) ^ 2 * l2 ^ 2 * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) * A(i,11) - 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) - 0.4e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,22) * s(i,23) - 0.2e1 / 0.3e1 * cos(s(i,8)) ^ 2 * l2 ^ 2 * m2 * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.4e1 * m3 * s(i,2) * sin(s(i,8)) * A(i,8) * l2 - 0.4e1 * m3 * s(i,2) * cos(s(i,8)) * s(i,20) ^ 2 * l2 - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,6)) * cos(s(i,5)) * A(i,5) + 0.4e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * A(i,3) - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * sin(s(i,10)) * cos(s(i,12)) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * sin(s(i,8)) * A(i,8) * l2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * cos(s(i,8)) * s(i,20) ^ 2 * l2 + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * sin(s(i,4)) * A(i,4) + 0.8e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) 0.4e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,19) * s(i,20) - 0.8e1 / 0.3e1 * m1 * cos(s(i,5)) * l1 ^ 2 * sin(s(i,5)) * sin(s(i,4)) * A(i,4) + 0.8e1 / 0.3e1 * m1 * sin(s(i,5)) ^ 2 * s(i,17) * l1 ^ 2 * sin(s(i,4)) * s(i,16) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) - 0.4e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * sin(s(i,7)) - 0.16e2 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,7)) * sin(s(i,9)) * s(i,21) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * cos(s(i,8)) ^ 2 * s(i,20) * b2 ^ 2 * m2 * s(i,19) * sin(s(i,7)) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 * b2 ^ 2 * m2 * s(i,19) * s(i,20) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9))

272 ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,9)) * cos(s(i,8)) * A(i,8) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,7)) * cos(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * cos(s(i,7)) * A(i,8) - 0.16e2 / 0.3e1 * cos(s(i,9)) * b2 ^ 2 * m2 * cos(s(i,7)) * s(i,20) * sin(s(i,9)) * s(i,21) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * sin(s(i,7)) * s(i,19) * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,11)) ^ 2 * s(i,23) * a3 ^ 2 * m3 * s(i,22) * sin(s(i,10)) 0.8e1 / 0.3e1 * sin(s(i,11)) ^ 2 * a3 ^ 2 * m3 * s(i,22) * s(i,23) * sin(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * cos(s(i,10)) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * sin(s(i,5)) * A(i,5) * l1 + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * cos(s(i,5)) * s(i,17) ^ 2 * l1 + 0.4e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * A(i,3) + 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,12)) * sin(s(i,10)) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * A(i,8) * cos(s(i,9)) ^ 2 + 0.4e1 * m1 * s(i,2) * sin(s(i,8)) * A(i,8) * l2 + 0.4e1 * m1 * s(i,2) * cos(s(i,8)) * s(i,20) ^ 2 * l2 + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,6)) * cos(s(i,5)) * A(i,5) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,4)) * cos(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,10)) * cos(s(i,11)) * s(i,23) 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * sin(s(i,10)) * s(i,24) * cos(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,10)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * A(i,10) * sin(s(i,12)) * cos(s(i,10)) - 0.8e1 / 0.3e1 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * s(i,24) * cos(s(i,10)) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) - 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,12)) * cos(s(i,10)) 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,12)) ^ 2 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * s(i,24) * cos(s(i,10)) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * sin(s(i,8)) * A(i,8) * l2 0.8e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + 0.4e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) - 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) ^ 2 * sin(s(i,12)) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * sin(s(i,10)) - 0.16e2 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,10)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * cos(s(i,11)) ^ 2 * s(i,23) * b3 ^ 2 * m3 * s(i,22) * sin(s(i,10)) - 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 * b3 ^ 2 * m3 * s(i,22) * s(i,23) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * cos(s(i,10)) - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,7)) * sin(s(i,8)) * A(i,9) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,7)) * s(i,19) * sin(s(i,8)) * s(i,21) + 0.8e1 * m1 * s(i,2) * A(i,3) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * cos(s(i,8)) * s(i,20) ^ 2 * l2 - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,7)) * cos(s(i,8)) *

273 s(i,20) * s(i,21) + 0.8e1 / 0.3e1 * cos(s(i,5)) ^ 2 * s(i,17) * a1 ^ 2 * m1 * s(i,16) * sin(s(i,4)) - 0.8e1 / 0.3e1 * sin(s(i,5)) ^ 2 * a1 ^ 2 * m1 * s(i,16) * s(i,17) * sin(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * cos(s(i,4)) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,10)) * sin(s(i,11)) * A(i,12) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,10)) * s(i,22) * sin(s(i,11)) * s(i,24) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,10)) * cos(s(i,11)) * s(i,23) * s(i,24) 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * sin(s(i,10)) * A(i,10) 0.8e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * s(i,23) * sin(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * sin(s(i,4)) * s(i,16) * l1 ^ 2 * m1 * s(i,17) - 0.2e1 * m1 * sin(s(i,7)) * s(i,19) * l2 ^ 2 * s(i,20) - 0.16e2 / 0.3e1 * cos(s(i,12)) * b3 ^ 2 * m3 * cos(s(i,10)) * s(i,23) * sin(s(i,12)) * s(i,24) - 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * sin(s(i,10)) * s(i,22) * s(i,23) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * A(i,11) * cos(s(i,12)) ^ 2 + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * s(i,22) * s(i,23) * cos(s(i,12)) ^ 2 + 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * s(i,23) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,12) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,11)) * s(i,23) * a3 ^ 2 * m3 * s(i,24) * sin(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,24) * cos(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,9)) ^ 2 + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * sin(s(i,7)) * cos(s(i,9)) * sin(s(i,8)) * s(i,20) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * A(i,7) * sin(s(i,9)) * cos(s(i,7)) - 0.8e1 / 0.3e1 * sin(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * s(i,21) * cos(s(i,7)) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * s(i,19) * s(i,20) * cos(s(i,9)) ^ 2 + 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * s(i,20) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * cos(s(i,7)) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,10)) * s(i,22) * l3 ^ 2 * m3 * s(i,23) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * s(i,19) * s(i,20) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * s(i,16) * s(i,17) - 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,9)) * cos(s(i,7)) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,9)) ^ 2 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * s(i,21) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,9)) * sin(s(i,7)) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,10)) * sin(s(i,12)) * cos(s(i,11)) * A(i,11) 0.4e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + 0.8e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,19) * s(i,20) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,6) * sin(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,5)) * s(i,17) * a1 ^ 2 * m1 * s(i,18) * sin(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,18) * cos(s(i,4)) * s(i,16) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * cos(s(i,4)) * A(i,5) - 0.16e2 / 0.3e1 * cos(s(i,6)) * b1 ^ 2 * m1 * cos(s(i,4)) * s(i,17) * sin(s(i,6)) * s(i,18) - 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.2e1 / 0.3e1 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * m2 * sin(s(i,7)) * s(i,19) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * sin(s(i,4)) - 0.8e1 / 0.3e1 * sin(s(i,8)) ^ 2 * a2 ^ 2 * m2 * s(i,19) * s(i,20) * sin(s(i,7)) - 0.2e1 * m3 * sin(s(i,7)) * s(i,19) * l2 ^ 2 * s(i,20) -

274 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 + 0.4e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * cos(s(i,10)) * A(i,11) 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * A(i,4) * sin(s(i,6)) * cos(s(i,4)) - 0.8e1 / 0.3e1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * s(i,18) * cos(s(i,4)) - 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) ^ 2 * sin(s(i,6)) * sin(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * sin(s(i,4)) 0.16e2 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * sin(s(i,4)) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * cos(s(i,5)) ^ 2 * s(i,17) * b1 ^ 2 * m1 * s(i,16) * sin(s(i,4)) - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 * b1 ^ 2 * m1 * s(i,16) * s(i,17) * sin(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * cos(s(i,4)) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * A(i,5) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * s(i,16) * s(i,17) * cos(s(i,6)) ^ 2 + 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * s(i,17) * cos(s(i,6)) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * cos(s(i,10)) * A(i,11) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,4)) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * sin(s(i,4)) * s(i,18) * cos(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,4)) * sin(s(i,6)) * sin(s(i,5)) * s(i,17) ^ 2 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * A(i,10) - 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * s(i,18) * cos(s(i,4)) - 0.8e1 * m1 * s(i,3) * A(i,2) 0.4e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * cos(s(i,10)) 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,6)) * sin(s(i,4)) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * s(i,22) * s(i,23) * cos(s(i,12)) ^ 2 + 0.4e1 * m3 * s(i,1) * sin(s(i,11)) * A(i,11) * l3 + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * cos(s(i,10)) * cos(s(i,11)) * s(i,23) 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * cos(s(i,10)) * s(i,24) * cos(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * cos(s(i,10)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) ^ 2 + 0.4e1 * m3 * s(i,1) * sin(s(i,8)) * A(i,8) * l2 + 0.4e1 * m3 * s(i,1) * cos(s(i,8)) * s(i,20) ^ 2 * l2 + 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) + 0.8e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,10)) * sin(s(i,11)) * A(i,12) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,10)) * s(i,22) * sin(s(i,11)) * s(i,24) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,10)) * cos(s(i,11)) * s(i,23) * s(i,24) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * A(i,5) * cos(s(i,6)) ^ 2 - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * s(i,16) * s(i,17) * cos(s(i,6)) ^ 2 + 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * s(i,17) * cos(s(i,6)) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * sin(s(i,4)) * A(i,5) - 0.16e2 / 0.3e1 * cos(s(i,6)) * b1 ^ 2 * m1 * sin(s(i,4)) * s(i,17) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * b1 ^ 2 * m1 * cos(s(i,4)) * s(i,16) * s(i,17) + 0.2e1 * m1 * cos(s(i,8)) ^ 2 * l2 ^ 2 * s(i,20) * cos(s(i,7)) * s(i,19) - 0.2e1 * m1 * cos(s(i,8))

275 * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * cos(s(i,10)) * A(i,10) - 0.8e1 / 0.3e1 * m3 * sin(s(i,11)) ^ 2 * s(i,23) * l3 ^ 2 * cos(s(i,10)) * s(i,22) + 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) ^ 2 * l3 ^ 2 * s(i,23) * cos(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * m3 * cos(s(i,11)) * l3 ^ 2 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.16e2 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * cos(s(i,10)) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) - 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,12)) * sin(s(i,10)) 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * sin(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,12)) ^ 2 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) * s(i,24) * sin(s(i,10)) - 0.8e1 / 0.3e1 * sin(s(i,12)) * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,12)) * cos(s(i,10)) + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * sin(s(i,8)) * A(i,8) * l2 + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * cos(s(i,8)) * s(i,20) ^ 2 * l2 - 0.8e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,4)) * sin(s(i,5)) * A(i,6) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,4)) * s(i,16) * sin(s(i,5)) * s(i,18) 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,4)) * cos(s(i,5)) * s(i,17) * s(i,18) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,7)) * sin(s(i,8)) * A(i,9) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,7)) * s(i,19) * sin(s(i,8)) * s(i,21) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,7)) * cos(s(i,8)) * s(i,20) * s(i,21) + 0.8e1 / 0.3e1 * sin(s(i,11)) ^ 2 * a3 ^ 2 * m3 * s(i,22) * s(i,23) * cos(s(i,10)) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) - 0.2e1 * m1 * cos(s(i,5)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * s(i,19) * s(i,20) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * cos(s(i,10)) * sin(s(i,12)) * cos(s(i,11)) * A(i,11) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * cos(s(i,4)) * s(i,18) * cos(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,6)) * sin(s(i,5)) * s(i,17) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,9)) * sin(s(i,7)) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * sin(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,9)) ^ 2 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * s(i,21) * sin(s(i,7)) - 0.8e1 / 0.3e1 * sin(s(i,9)) * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,9)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,4)) * s(i,16) * s(i,17) + 0.2e1 * m1 * cos(s(i,7)) * s(i,19) * l2 ^ 2 * s(i,20) + 0.2e1 * m3 * cos(s(i,7)) * s(i,19) * l2 ^ 2 * s(i,20) + 0.8e1 / 0.3e1 * cos(s(i,4)) * s(i,16) * l1 ^ 2 * m1 * s(i,17) + 0.2e1 * m1 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.2e1 * m1 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * cos(s(i,7)) * s(i,19) + 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * A(i,7) * sin(s(i,9)) * sin(s(i,7)) - 0.8e1 / 0.3e1 * sin(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * s(i,21) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) ^ 2 * sin(s(i,9)) * cos(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * sin(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,5)) ^ 2 * l1 ^ 2 * m1 * s(i,17) * cos(s(i,4)) * s(i,16) - 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) + 0.2e1 / 0.3e1 * cos(s(i,8)) ^ 2 * l2 ^ 2 * m2 * s(i,20) * cos(s(i,7)) * s(i,19) + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m1 * sin(s(i,8)) *

276 sin(s(i,7)) * l2 * sin(s(i,5)) * A(i,5) * l1 + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * cos(s(i,5)) * s(i,17) ^ 2 * l1 + 0.4e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * A(i,3) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * sin(s(i,8)) * A(i,8) * l2 - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * cos(s(i,5)) ^ 2 * s(i,17) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * sin(s(i,4)) + 0.4e1 * m3 * s(i,3) * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * cos(s(i,10)) * A(i,10) - 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 - 0.4e1 * m3 * s(i,3) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * A(i,4) * sin(s(i,6)) * sin(s(i,4)) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * cos(s(i,10)) * sin(s(i,12)) * cos(s(i,11)) * A(i,11) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * cos(s(i,10)) * cos(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * cos(s(i,10)) * s(i,24) * cos(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * cos(s(i,10)) * sin(s(i,12)) * sin(s(i,11)) * s(i,23) ^ 2 - 0.4e1 * m1 * s(i,1) * sin(s(i,8)) * A(i,8) * l2 - 0.4e1 * m1 * s(i,1) * cos(s(i,8)) * s(i,20) ^ 2 * l2 - 0.4e1 * m1 * s(i,1) * sin(s(i,5)) * A(i,5) * l1 - 0.4e1 * m1 * s(i,1) * cos(s(i,5)) * s(i,17) ^ 2 * l1 + 0.4e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * A(i,3) + 0.8e1 / 0.3e1 * cos(s(i,5)) * l1 ^ 2 * m1 * sin(s(i,5)) * cos(s(i,4)) * A(i,4) - 0.8e1 / 0.3e1 * sin(s(i,5)) ^ 2 * s(i,17) * l1 ^ 2 * m1 * cos(s(i,4)) * s(i,16) - 0.8e1 / 0.3e1 * cos(s(i,5)) * l1 ^ 2 * m1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * A(i,10) * sin(s(i,12)) * sin(s(i,10)) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,10)) * s(i,22) * s(i,23) - 0.2e1 / 0.3e1 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * m2 * cos(s(i,7)) * s(i,19) - 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * A(i,8) * cos(s(i,9)) ^ 2 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,7)) * s(i,19) * s(i,20) * cos(s(i,9)) ^ 2 + 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * s(i,20) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,9) * cos(s(i,7)) - 0.8e1 / 0.3e1 * cos(s(i,8)) * s(i,20) * a2 ^ 2 * m2 * s(i,21) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,21) * sin(s(i,7)) * s(i,19) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * sin(s(i,7)) * A(i,8) - 0.16e2 / 0.3e1 * cos(s(i,9)) * b2 ^ 2 * m2 * sin(s(i,7)) * s(i,20) * sin(s(i,9)) * s(i,21) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) * b2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * cos(s(i,7)) + 0.16e2 / 0.3e1 * cos(s(i,9)) * sin(s(i,8)) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * cos(s(i,7)) * sin(s(i,9)) * s(i,21) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,9)) * cos(s(i,8)) * A(i,8) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * s(i,21) * cos(s(i,7)) * cos(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * cos(s(i,7)) * s(i,21) * cos(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,9)) * sin(s(i,8)) * s(i,20) ^ 2 + 0.4e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * sin(s(i,10)) * A(i,11) 0.8e1 / 0.3e1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * sin(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * s(i,18) * sin(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) ^ 2 * sin(s(i,6)) * cos(s(i,4)) - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) * b1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * cos(s(i,4)) + 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * sin(s(i,5)) ^ 2 * b1 ^ 2 * m1 * s(i,16) * s(i,17) * cos(s(i,4)) +

277 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,24) * sin(s(i,10)) * s(i,22) - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,6) * cos(s(i,4)) - 0.8e1 / 0.3e1 * cos(s(i,5)) * s(i,17) * a1 ^ 2 * m1 * s(i,18) * cos(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,18) * sin(s(i,4)) * s(i,16) + 0.2e1 / 0.3e1 * cos(s(i,7)) * s(i,19) * l2 ^ 2 * m2 * s(i,20) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,6)) * cos(s(i,5)) * A(i,5) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * s(i,18) * cos(s(i,4)) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * cos(s(i,4)) * s(i,18) * cos(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,6)) * sin(s(i,5)) * s(i,17) ^ 2 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) * cos(s(i,4)) * cos(s(i,6)) * cos(s(i,5)) * A(i,5) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * s(i,18) * cos(s(i,4)) * cos(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,9)) * cos(s(i,8)) * A(i,8) 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * s(i,21) * cos(s(i,7)) * cos(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * cos(s(i,7)) * s(i,21) * cos(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) * cos(s(i,7)) * sin(s(i,9)) * sin(s(i,8)) * s(i,20) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * sin(s(i,7)) * cos(s(i,9)) ^ 2 - 0.16e2 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * A(i,5) + 0.4e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * s(i,23) * cos(s(i,10)) * s(i,22) + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) * A(i,11) - 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,4)) * A(i,5) + 0.2e1 * m3 * sin(s(i,7)) * l2 ^ 2 * A(i,8) + 0.4e1 * m3 * cos(s(i,8)) * l2 * A(i,1) + 0.4e1 * m3 * cos(s(i,11)) * l3 * A(i,1) - 0.4e1 * m1 * cos(s(i,8)) * l2 * A(i,1) - 0.4e1 * m1 * cos(s(i,5)) * l1 * A(i,1) + 0.8e1 / 0.3e1 * sin(s(i,4)) * l1 ^ 2 * m1 * A(i,5) + 0.2e1 / 0.3e1 * sin(s(i,7)) * l2 ^ 2 * m2 * A(i,8) + 0.2e1 * m1 * sin(s(i,7)) * l2 ^ 2 * A(i,8) + 0.8e1 * m3 * s(i,3) * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,22) * s(i,23) 0.8e1 / 0.3e1 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * s(i,24) * sin(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) ^ 2 * sin(s(i,12)) * cos(s(i,10)) - 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * cos(s(i,10)) 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * cos(s(i,11)) ^ 2 * s(i,23) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,10)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) ^ 2 * b3 ^ 2 * m3 * s(i,22) * s(i,23) * cos(s(i,10)) 0.4e1 * m1 * s(i,3) * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) + 0.4e1 * m1 * s(i,3) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * cos(s(i,4)) * A(i,4) - 0.8e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 - 0.4e1 * m1 * s(i,3) * l1 * cos(s(i,5)) * sin(s(i,4)) * A(i,5) + 0.4e1 * m1 * s(i,3) * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) + 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.2e1 * m3 * sin(s(i,8)) ^ 2 * s(i,20) * l2 ^ 2 * cos(s(i,7)) * s(i,19) + 0.2e1 * m3 * cos(s(i,8)) ^ 2 * l2 ^ 2 * s(i,20) * cos(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,8)) * l2 ^ 2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * A(i,10) + 0.4e1 * m3 * s(i,1) * cos(s(i,11)) * s(i,23) ^ 2 * l3 - 0.4e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * A(i,3) + 0.2e1 * m3 *

278 sin(s(i,8)) * sin(s(i,7)) * l2 * sin(s(i,11)) * A(i,11) * l3 + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * cos(s(i,11)) * s(i,23) ^ 2 * l3 0.4e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * A(i,3) - 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) - 0.4e1 * m3 * s(i,3) * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) + 0.8e1 * m1 * s(i,3) * A(i,1) + 0.16e2 / 0.3e1 * cos(s(i,12)) * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * cos(s(i,10)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,7)) * A(i,8) + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * b2 ^ 2 * m2 * cos(s(i,7)) * s(i,19) * s(i,20) + 0.8e1 / 0.3e1 * cos(s(i,10)) * s(i,22) * l3 ^ 2 * m3 * s(i,23) + 0.2e1 / 0.3e1 * cos(s(i,8)) * l2 ^ 2 * m2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * cos(s(i,8)) ^ 2 * s(i,20) * b2 ^ 2 * m2 * s(i,19) * cos(s(i,7)) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * sin(s(i,11)) * b3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * sin(s(i,10)) - 0.8e1 / 0.3e1 * cos(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * sin(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,6)) ^ 2 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * s(i,18) * sin(s(i,4)) - 0.8e1 / 0.3e1 * sin(s(i,6)) * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,6)) * cos(s(i,4)) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * A(i,11) * cos(s(i,12)) ^ 2 + 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * s(i,23) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * cos(s(i,5)) ^ 2 * s(i,17) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,4)) * cos(s(i,6)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,5)) ^ 2 * a1 ^ 2 * m1 * s(i,16) * s(i,17) * cos(s(i,4)) * cos(s(i,6)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * sin(s(i,4)) * cos(s(i,6)) ^ 2 - 0.16e2 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,6)) * sin(s(i,6)) * s(i,18) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * sin(s(i,10)) * A(i,11) - 0.16e2 / 0.3e1 * cos(s(i,12)) * b3 ^ 2 * m3 * sin(s(i,10)) * s(i,23) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * cos(s(i,12)) ^ 2 * b3 ^ 2 * m3 * cos(s(i,10)) * s(i,22) * s(i,23) - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,12) * cos(s(i,10)) - 0.8e1 / 0.3e1 * cos(s(i,11)) * s(i,23) * a3 ^ 2 * m3 * s(i,24) * cos(s(i,10)) - 0.8e1 / 0.3e1 * cos(s(i,11)) ^ 2 * s(i,23) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * sin(s(i,10)) + 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) * cos(s(i,10)) * cos(s(i,12)) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,11)) ^ 2 * s(i,23) * a3 ^ 2 * m3 * s(i,22) * cos(s(i,10)) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,11)) * a3 ^ 2 * m3 * s(i,22) ^ 2 * cos(s(i,11)) * sin(s(i,10)) * cos(s(i,12)) ^ 2 + 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * A(i,4) + 0.4e1 * m1 * cos(s(i,8)) * l2 * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) - 0.2e1 * m1 * cos(s(i,8)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,11)) ^ 2 * a3 ^ 2 * m3 * s(i,22) * s(i,23) * cos(s(i,10)) * cos(s(i,12)) ^ 2 + 0.8e1 / 0.3e1 * sin(s(i,10)) * l3 ^ 2 * m3 * A(i,11) - 0.8e1 * m1 * s(i,1) * A(i,3) + 0.8e1 * s(i,3) * m2 * A(i,1) - 0.8e1 * m3 * s(i,1) * A(i,3) + 0.8e1 * m3 * s(i,3) * A(i,1) - 0.8e1 * s(i,1) * m2 * A(i,3) 0.2e1 * m3 * cos(s(i,8)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,10)) * A(i,11) 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * cos(s(i,4)) - 0.8e1 / 0.3e1 * cos(s(i,5)) ^ 2 * s(i,17) * a1 ^ 2 * m1 * s(i,16) * cos(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) ^ 2 * a1 ^ 2 * m1 * s(i,16) * s(i,17) * cos(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * s(i,16) ^ 2 * cos(s(i,5)) * sin(s(i,4)) + 0.8e1 / 0.3e1 * sin(s(i,5)) * a1 ^ 2 * m1 * A(i,4) * cos(s(i,5)) * cos(s(i,4)) * cos(s(i,6)) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,9)) ^ 2 * sin(s(i,8)) ^ 2 *

279 b2 ^ 2 * m2 * s(i,19) * s(i,20) * cos(s(i,7)) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * cos(s(i,8)) * s(i,20) ^ 2 * l2 - 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * cos(s(i,7)) - 0.8e1 / 0.3e1 * cos(s(i,8)) ^ 2 * s(i,20) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) ^ 2 * a2 ^ 2 * m2 * s(i,19) * s(i,20) * cos(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * s(i,19) ^ 2 * cos(s(i,8)) * sin(s(i,7)) + 0.8e1 / 0.3e1 * sin(s(i,8)) * a2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) * cos(s(i,7)) * cos(s(i,9)) ^ 2 + 0.8e1 / 0.3e1 * cos(s(i,8)) ^ 2 * s(i,20) * a2 ^ 2 * m2 * s(i,19) * cos(s(i,7)) * cos(s(i,9)) ^ 2 - 0.8e1 / 0.3e1 * sin(s(i,8)) ^ 2 * a2 ^ 2 * m2 * s(i,19) * s(i,20) * cos(s(i,7)) * cos(s(i,9)) ^ 2 + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) + 0.4e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) - 0.2e1 * m3 * cos(s(i,11)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + 0.16e2 / 0.3e1 * cos(s(i,6)) * sin(s(i,5)) * b1 ^ 2 * m1 * s(i,16) * cos(s(i,5)) * cos(s(i,4)) * sin(s(i,6)) * s(i,18) 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * sin(s(i,10)) * A(i,11) + 0.4e1 * m3 * s(i,1) * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * s(i,21) * sin(s(i,8)) * s(i,20) + 0.2e1 * m3 * l2 ^ 2 * A(i,7) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * A(i,7) - 0.8e1 * m3 * s(i,2) * A(i,1) + 0.8e1 / 0.3e1 * m1 * l1 ^ 2 * A(i,4) + 0.8e1 * m1 * s(i,1) * A(i,2) - 0.8e1 * m1 * s(i,2) * A(i,1) + 0.8e1 * s(i,1) * m2 * A(i,2) - 0.8e1 * s(i,2) * m2 * A(i,1) + 0.8e1 * m3 * s(i,1) * A(i,2) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * A(i,10) + 0.8e1 / 0.3e1 * l3 ^ 2 * m3 * A(i,10) + 0.2e1 / 0.3e1 * l2 ^ 2 * m2 * A(i,7) + 0.2e1 * m1 * l2 ^ 2 * A(i,7) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * A(i,4) - 0.2e1 * m1 * l2 ^ 2 * A(i,7) * cos(s(i,8)) ^ 2 - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * A(i,4) * cos(s(i,6)) ^ 2 - 0.2e1 * m3 * l2 ^ 2 * A(i,7) * cos(s(i,8)) ^ 2 + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,11)) * A(i,12) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * A(i,9) * cos(s(i,8)) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) ^ 2 * A(i,10) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * A(i,10) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * A(i,4) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * A(i,10) * cos(s(i,12)) ^ 2 - 0.8e1 / 0.3e1 * m1 * l1 ^ 2 * A(i,4) * cos(s(i,5)) ^ 2 - 0.8e1 / 0.3e1 * l3 ^ 2 * m3 * A(i,10) * cos(s(i,11)) ^ 2 - 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * A(i,7) * cos(s(i,9)) ^ 2 + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * A(i,7) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,5)) * A(i,6) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) ^ 2 * A(i,4) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) * A(i,12) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * A(i,9) * cos(s(i,8)) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) * A(i,6) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) ^ 2 * A(i,7) - 0.2e1 / 0.3e1 * l2 ^ 2 * m2 * A(i,7) * cos(s(i,8)) ^ 2 + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - 0.4e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * A(i,1) + 0.4e1 * m3 * s(i,2) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) - 0.4e1 * m3 * s(i,2) * l3 * sin(s(i,11)) * cos(s(i,10)) * A(i,10) - 0.8e1 * m3 * s(i,2) * l3 * cos(s(i,11)) * s(i,23) * cos(s(i,10)) * s(i,22) + 0.4e1 * m3 * s(i,2) * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 - 0.4e1 * m3 * s(i,2) * l3 * cos(s(i,11)) * sin(s(i,10)) * A(i,11) + 0.4e1 * m3 * s(i,2) * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * A(i,4) + 0.4e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * A(i,1) + 0.16e2 / 0.3e1 * m1 * l1

280 ^ 2 * s(i,16) * cos(s(i,5)) * sin(s(i,5)) * s(i,17) + 0.16e2 / 0.3e1 * l3 ^ 2 * m3 * s(i,22) * cos(s(i,11)) * sin(s(i,11)) * s(i,23) + 0.16e2 / 0.3e1 * b2 ^ 2 * m2 * s(i,19) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) 0.4e1 * m1 * s(i,1) * l1 * sin(s(i,5)) * sin(s(i,4)) * A(i,4) - 0.8e1 * m1 * s(i,1) * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) 0.4e1 * m1 * s(i,1) * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 + 0.4e1 * m1 * s(i,1) * l1 * cos(s(i,5)) * cos(s(i,4)) * A(i,5) - 0.4e1 * m1 * s(i,1) * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - 0.4e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * A(i,2) + 0.4e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) * s(i,19) * s(i,20) 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) - 0.16e2 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * cos(s(i,5)) ^ 2 * s(i,16) * sin(s(i,6)) * s(i,18) + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) + 0.4e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * sin(s(i,4)) * A(i,5) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,11)) * s(i,23) * s(i,24) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * s(i,21) * sin(s(i,8)) * s(i,20) - 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * s(i,22) * sin(s(i,12)) * s(i,24) - 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * s(i,16) * sin(s(i,6)) * s(i,18) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) ^ 2 * A(i,4) * cos(s(i,6)) ^ 2 + 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) * s(i,16) * cos(s(i,6)) ^ 2 * sin(s(i,5)) * s(i,17) + 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) ^ 2 * s(i,16) * cos(s(i,6)) * sin(s(i,6)) * s(i,18) + 0.4e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 0.4e1 * m3 * s(i,1) * l3 * cos(s(i,11)) * cos(s(i,10)) * A(i,11) + 0.4e1 * m3 * s(i,1) * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) + 0.8e1 * m3 * s(i,1) * l3 * cos(s(i,11)) * sin(s(i,10)) * s(i,22) * s(i,23) + 0.4e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * A(i,2) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,9)) * sin(s(i,8)) * A(i,8) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) + 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,9)) * cos(s(i,8)) * s(i,20) ^ 2 - 0.4e1 * m1 * s(i,2) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + 0.4e1 * m1 * s(i,2) * l1 * sin(s(i,5)) * cos(s(i,4)) * A(i,4) + 0.8e1 * m1 * s(i,2) * l1 * cos(s(i,5)) * s(i,17) * cos(s(i,4)) * s(i,16) - 0.4e1 * m1 * s(i,2) * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 + 0.4e1 * m1 * s(i,2) * l1 * cos(s(i,5)) * sin(s(i,4)) * A(i,5) - 0.4e1 * m1 * s(i,2) * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) + 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * A(i,10) - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * s(i,22) ^ 2 + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) + 0.4e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) + 0.4e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * s(i,17) * sin(s(i,4)) * s(i,16) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * s(i,16) ^ 2 - 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * A(i,5) + 0.2e1 * m1 * sin(s(i,8)) * sin(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * cos(s(i,4)) - 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * sin(s(i,4)) * s(i,16) ^ 2 - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,11)) * s(i,23) *

281 s(i,24) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * cos(s(i,8)) ^ 2 * A(i,7) - 0.16e2 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) * cos(s(i,8)) ^ 2 * s(i,19) * sin(s(i,9)) * s(i,21) - 0.16e2 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * cos(s(i,8)) * s(i,19) * sin(s(i,8)) * s(i,20) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * sin(s(i,11)) * A(i,11) + 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * cos(s(i,11)) * s(i,23) ^ 2 + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * cos(s(i,5)) ^ 2 * A(i,4) 0.4e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * A(i,2) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * sin(s(i,10)) + 0.4e1 * m3 * s(i,1) * l3 * sin(s(i,11)) * sin(s(i,10)) * A(i,10) + 0.4e1 * m3 * s(i,1) * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 + 0.4e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * A(i,1) + 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * cos(s(i,4)) * A(i,4) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) + 0.2e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) 0.4e1 * m3 * s(i,2) * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.8e1 * m3 * s(i,2) * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) + 0.4e1 * m3 * s(i,2) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 0.4e1 * m3 * s(i,2) * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) - 0.2e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * sin(s(i,5)) * s(i,17) ^ 2 * sin(s(i,4)) + 0.4e1 * m1 * sin(s(i,8)) * cos(s(i,7)) * l2 * l1 * cos(s(i,5)) * cos(s(i,4)) * s(i,16) * s(i,17) - 0.4e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * A(i,1) - 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) * s(i,22) * sin(s(i,11)) * s(i,23) + 0.4e1 * m3 * sin(s(i,8)) * cos(s(i,7)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) * s(i,22) * s(i,23) + 0.4e1 * m3 * l2 ^ 2 * s(i,19) * cos(s(i,8)) * sin(s(i,8)) * s(i,20) - 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 - 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) + 0.2e1 * m1 * sin(s(i,5)) * sin(s(i,4)) * l1 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + 0.4e1 * m1 * s(i,2) * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) + 0.8e1 * m1 * s(i,2) * l2 * cos(s(i,8)) * s(i,20) * cos(s(i,7)) * s(i,19) - 0.4e1 * m1 * s(i,2) * l2 * sin(s(i,8)) * sin(s(i,7)) * s(i,19) ^ 2 + 0.4e1 * m1 * s(i,2) * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * sin(s(i,10)) * A(i,10) + 0.4e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * s(i,23) * sin(s(i,10)) * s(i,22) + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * cos(s(i,10)) * s(i,22) ^ 2 + 0.4e1 * m3 * sin(s(i,11)) * sin(s(i,10)) * l3 * A(i,2) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * sin(s(i,9)) * cos(s(i,9)) * sin(s(i,8)) * A(i,8) + 0.8e1 / 0.3e1 * b2 ^ 2 * m2 * cos(s(i,9)) ^ 2 * s(i,21) * sin(s(i,8)) * s(i,20) - 0.16e2 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * cos(s(i,5)) * s(i,16) * sin(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * sin(s(i,5)) * A(i,5) + 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * cos(s(i,5)) * s(i,17) ^ 2 + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * sin(s(i,5)) * A(i,5) - 0.8e1

282 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) ^ 2 * s(i,18) * sin(s(i,5)) * s(i,17) + 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * cos(s(i,6)) * sin(s(i,6)) * cos(s(i,5)) * s(i,17) ^ 2 + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * sin(s(i,11)) * A(i,11) - 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * sin(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * s(i,24) * sin(s(i,11)) * s(i,23) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * sin(s(i,12)) * cos(s(i,11)) * s(i,23) ^ 2 - 0.8e1 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) ^ 2 * A(i,7) * cos(s(i,9)) ^ 2 + 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) * s(i,19) * cos(s(i,9)) ^ 2 * sin(s(i,8)) * s(i,20) - 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * cos(s(i,11)) * cos(s(i,10)) * A(i,11) + 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) ^ 2 * s(i,19) * cos(s(i,9)) * sin(s(i,9)) * s(i,21) + 0.2e1 * m3 * sin(s(i,8)) * sin(s(i,7)) * l2 * l3 * sin(s(i,11)) * s(i,23) ^ 2 * cos(s(i,10)) - 0.8e1 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) ^ 2 * A(i,10) * cos(s(i,12)) ^ 2 + 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) * s(i,22) * cos(s(i,12)) ^ 2 * sin(s(i,11)) * s(i,23) - 0.4e1 * m1 * s(i,1) * l2 * sin(s(i,8)) * sin(s(i,7)) * A(i,7) - 0.8e1 * m1 * s(i,1) * l2 * cos(s(i,8)) * s(i,20) * sin(s(i,7)) * s(i,19) - 0.4e1 * m1 * s(i,1) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 - 0.4e1 * m3 * s(i,1) * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) + 0.4e1 * m3 * s(i,1) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + 0.8e1 * m3 * s(i,1) * l2 * cos(s(i,8)) * sin(s(i,7)) * s(i,19) * s(i,20) + 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * cos(s(i,8)) * sin(s(i,7)) * A(i,8) - 0.2e1 * m3 * sin(s(i,11)) * cos(s(i,10)) * l3 * l2 * sin(s(i,8)) * s(i,20) ^ 2 * sin(s(i,7)) + 0.4e1 * m1 * s(i,1) * l2 * cos(s(i,8)) * cos(s(i,7)) * A(i,8) - 0.4e1 * m1 * s(i,1) * l2 * sin(s(i,8)) * s(i,20) ^ 2 * cos(s(i,7)) + 0.16e2 / 0.3e1 * b3 ^ 2 * m3 * s(i,22) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) - 0.8e1 / 0.3e1 * b1 ^ 2 * m1 * sin(s(i,5)) * s(i,17) * s(i,18) - 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,9)) * s(i,19) * sin(s(i,9)) * s(i,21) - 0.16e2 / 0.3e1 * a1 ^ 2 * m1 * cos(s(i,5)) * s(i,16) * sin(s(i,5)) * s(i,17) + 0.16e2 / 0.3e1 * a3 ^ 2 * m3 * cos(s(i,11)) ^ 2 * s(i,22) * cos(s(i,12)) * sin(s(i,12)) * s(i,24) + 0.8e1 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * cos(s(i,11)) ^ 2 * A(i,10) - 0.16e2 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) * cos(s(i,11)) ^ 2 * s(i,22) * sin(s(i,12)) * s(i,24) 0.16e2 / 0.3e1 * b3 ^ 2 * m3 * cos(s(i,12)) ^ 2 * cos(s(i,11)) * s(i,22) * sin(s(i,11)) * s(i,23) + 0.4e1 * m3 * s(i,1) * l2 * sin(s(i,8)) * cos(s(i,7)) * s(i,19) ^ 2 + 0.2e1 * m1 * sin(s(i,5)) * cos(s(i,4)) * l1 * l2 * sin(s(i,8)) * cos(s(i,7)) * A(i,7) - 0.8e1 / 0.3e1 * a1 ^ 2 * m1 * sin(s(i,5)) * s(i,17) * s(i,18) - 0.16e2 / 0.3e1 * a2 ^ 2 * m2 * cos(s(i,8)) * s(i,19) * sin(s(i,8)) * s(i,20) + 0.4e1 / 0.3e1 * l2 ^ 2 * m2 * s(i,19) * cos(s(i,8)) * sin(s(i,8)) * s(i,20) + 0.4e1 * m1 * l2 ^ 2 * s(i,19) * cos(s(i,8)) * sin(s(i,8)) * s(i,20) + 0.16e2 / 0.3e1 * b1 ^ 2 * m1 * s(i,16) * cos(s(i,6)) * sin(s(i,6)) * s(i,18)]; %Torque on the rods about the origin T(i,:) = [-0.4e1 * g * ((2 * m1 * s(i,2)) + m1 * sin(s(i,8)) * cos(s(i,7)) * l2 + sin(s(i,5)) * cos(s(i,4)) * l1 * m1 + (2 * s(i,2) * m2) + (2 * m3 * s(i,2)) - m3 * sin(s(i,8)) * cos(s(i,7)) * l2 sin(s(i,11)) * cos(s(i,10)) * l3 * m3) 0.4e1 * g * ((2 * m1 * s(i,1)) m1 * sin(s(i,8)) * sin(s(i,7)) * l2 - sin(s(i,5)) * sin(s(i,4)) * l1 * m1 + (2 * s(i,1) * m2) + (2 * m3 * s(i,1)) + m3 * sin(s(i,8)) * sin(s(i,7)) * l2 + sin(s(i,11)) * sin(s(i,10)) * l3 * m3) 0];

283

end

Plot Generation – Plots.m %This is a combination of the Matlab generated code for the plots function Plots(X,s,V,t,w1,w2,w3,P,L,Ldot,T,JA1,JA2,CR1,CR2,T1,T3) %COMs %________________________________________________ %Assign the variables from the X matrix x1 = X(:,1); y1 = X(:,2); z1 = X(:,3); x2 = X(:,4); y2 = X(:,5); z2 = X(:,6); x3 = X(:,7); y3 = X(:,8); z3 = X(:,9); xs = X(:,10); ys = X(:,11); zs = X(:,12);

%% Create figure figure; hold on %% Create plot for plot3(x1,y1,z1,'Color',[0 0 1],'LineWidth',2); %% Create plot3 plot3(x2,y2,z2,'Color',[1 0 0],'LineWidth',2); %% Create plot3 plot3(x3,y3,z3,'Color',[0 1 0],'LineWidth',2); %%Create plot4 plot3(xs,ys,zs,'Color',[.5 .5 .5],'LineWidth',2); %Label the plot title('System Centers of Mass (COM)'); xlabel('X Position (m)'); ylabel('Y Position (m)'); zlabel('Z Position (m)');

284 view([-37.5 30]); grid('on'); %Compute the Min and max values for axes %X minx =min( min( [x1,x2,x3])); maxx =max( max( [x1,x2,x3])); %Y miny =min( min( [y1,y2,y3])); maxy =max( max( [y1,y2,y3])); %Z minz =min( min( [z1,z2,z3])); maxz =max( max( [z1,z2,z3])); %Set xlim ylim zlim

the axes limits = [minx,maxx]; = [miny,maxy]; = [minz,maxz];

%Create the legend legend({'Rod 1 COM','Rod 2 COM','Rod 3 COM','System COM'}); hold off %Euler Angles %___________________________________________________ %Data x1 y1 y2 y3

= = = =

t; s(:,4:6)*180/pi; s(:,7:9)*180/pi; s(:,10:12)*180/pi;

%

Auto-generated by MATLAB on 18-Aug-2008 19:17:21

%% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.13 0.589 0.3347 0.336],'Parent',figure1); title(axes1,'Rod 1 Euler Angles'); xlabel(axes1,'Time (s)'); ylabel(axes1,'Angle (Deg)'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2);

285 set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create axes axes2 = axes('Position',[0.5703 0.589 0.3347 0.336],'Parent',figure1); title(axes2,'Rod 2 Euler Angles'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Angle (Deg)'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create axes axes3 = axes('Position',[0.3443 0.1124 0.3347 0.3412],'Parent',figure1); title(axes3,'Rod 3 Euler Angles'); xlabel(axes3,'Time (s)'); ylabel(axes3,'Angle (Deg)'); box(axes3,'on'); hold(axes3,'all'); %% Create multiple lines using matrix input to plot plot3a = plot(x1,y3); set(plot3a(1),'LineWidth',2); set(plot3a(2),'LineWidth',2); set(plot3a(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'phi','theta','psi'},'Location','Best'); %% Create legend legend2 = legend(axes2,{'phi','theta','psi'},'Location','Best'); %% Create legend legend3 = legend(axes3,{'phi','theta','psi'},'Location','Best');

%Velocity Plots %___________________________________________________ %CREATEFIGURE(X1,Y1,Y2,Y3,Y4) % X1: vector of x data x1 = t; % Y1: matrix of y data y1 = V(:,1:3); % Y2: matrix of y data y2 = V(:,4:6);

286

% Y3: matrix of y data y3 = V(:,7:9); % Y4: matrix of y data y4 = V(:,10:12); %

Auto-generated by MATLAB on 23-May-2008 18:53:52

%% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.13 0.5838 0.3347 0.3412],'Parent',figure1); title(axes1,'Rod 1 COM Velocities'); xlabel(axes1,'Time (s)'); ylabel(axes1,'Velocity (m/s)'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best'); %% Create axes axes2 = axes('Position',[0.5703 0.5838 0.3347 0.3412],'Parent',figure1); title(axes2,'Rod 2 COM Velocities'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Velocity (m/s)'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create legend legend2 = legend(axes2,{'X','Y','Z'},'Location','Best'); %% Create axes axes3 = axes('Position',[0.13 0.11 0.3347 0.3412],'Parent',figure1); title(axes3,'Rod 3 COM Velocities'); xlabel(axes3,'Time (s)'); ylabel(axes3,'Velocity (m/s)'); box(axes3,'on'); hold(axes3,'all');

287

%% Create multiple lines using matrix input to plot plot3a = plot(x1,y3); set(plot3a(1),'LineWidth',2); set(plot3a(2),'LineWidth',2); set(plot3a(3),'LineWidth',2); %% Create legend legend3 = legend(axes3,{'X','Y','Z'},'Location','Best'); %% Create axes axes4 = axes('Position',[0.5703 0.11 0.3347 0.3412],'Parent',figure1); title(axes4,'System COM Velocities'); xlabel(axes4,'Time (s)'); ylabel(axes4,'Velocity (m/s)'); box(axes4,'on'); hold(axes4,'all'); %% Create multiple lines using matrix input to plot plot4 = plot(x1,y4); set(plot4(1),'LineWidth',2); set(plot4(2),'LineWidth',2); set(plot4(3),'LineWidth',2); %% Create legend legend4 = legend(axes4,{'X','Y','Z'},'Location','Best'); % Body Angular Velocity Plots %___________________________________________________ %CREATEFIGURE(X1,Y1,Y2,Y3,Y4) % X1: vector of x data x1 = t; % Y1: matrix of y data y1 = w1*180/pi; % Y2: matrix of y data y2 = w2*180/pi; % Y3: matrix of y data y3 = w3*180/pi; %


%% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.13 0.5838 0.3347 0.3412],'Parent',figure1); title(axes1,'Rod 1 Body Angular Velocities'); xlabel(axes1,'Time (s)'); ylabel(axes1,'Angular Velocity (deg/s)'); box(axes1,'on');

288 hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best'); %% Create axes axes2 = axes('Position',[0.5703 0.5838 0.3347 0.3412],'Parent',figure1); title(axes2,'Rod 2 Body Angular Velocities'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Angular Velocity (deg/s)'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create legend legend2 = legend(axes2,{'X','Y','Z'},'Location','Best'); %% Create axes axes3 = axes('Position',[0.13 0.11 0.3347 0.3412],'Parent',figure1); title(axes3,'Rod 3 Body Angular Velocities'); xlabel(axes3,'Time (s)'); ylabel(axes3,'Angular Velocity (deg/s)'); box(axes3,'on'); hold(axes3,'all'); %% Create multiple lines using matrix input to plot plot3a = plot(x1,y3); set(plot3a(1),'LineWidth',2); set(plot3a(2),'LineWidth',2); set(plot3a(3),'LineWidth',2); %% Create legend legend3 = legend(axes3,{'X','Y','Z'},'Location','Best'); %Joint Angles & Cross Products %___________________________________________________ %Data x1 = t; y1 = CR1; y2 = CR2; y3 = [JA1,JA2];

289 %% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.1348 0.589 0.3299 0.336],'Parent',figure1); title(axes1,'Cross Product (z1-z2)'); xlabel(axes1,'Time (s)'); ylabel(axes1,'Component Magnitude'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create axes axes2 = axes('Position',[0.5751 0.589 0.3299 0.336],'Parent',figure1); title(axes2,'Cross Product (z2-z3)'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Component Magnitude'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create axes axes3 = axes('Position',[0.13 0.11 0.7771 0.3412],'Parent',figure1); title(axes3,'Joint Angles'); xlabel(axes3,'Time (s)'); ylabel(axes3,'Angle (Deg)'); box(axes3,'on'); hold(axes3,'all'); %% Create multiple lines using matrix input to plot plot3a = plot(x1,y3); set(plot3a(1),'LineWidth',2); set(plot3a(2),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best'); %% Create legend legend2 = legend(axes2,{'X','Y','Z'},'Location','Best'); %% Create legend legend3 = legend(axes3,{'z1-z2 Angle','z2-z3 Angle'},'Location','Best'); %Torques

290 %___________________________________________________ %Data x1=t; y1=T1; y2=T3; %

Auto-generated by MATLAB on 18-Aug-2008 18:56:59

%% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.13 0.589 0.775 0.3286],'Parent',figure1); title(axes1,'T1(z1-z2) - Components about the Spatial Axes'); xlabel(axes1,'Time (s)'); ylabel(axes1,'Component Magnitude (Nm)'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create axes axes2 = axes('Position',[0.13 0.1152 0.775 0.3286],'Parent',figure1); title(axes2,'T3 (z2-z3) - Components about the Spatial Axes'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Component Magnitude (Nm)'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best'); %% Create legend legend2 = legend(axes2,{'X','Y','Z'},'Location','Best');

% Linear Momentum %___________________________________________________ %CREATEFIGURE(X1,Y1) % X1: vector of x data % Y1: matrix of y data

291 %

Auto-generated by MATLAB on 17-Jun-2008 23:42:25

x1 = t; y1 = P; %% Create figure figure1 = figure; %% Create axes axes1 = axes('Parent',figure1); title(axes1,'Linear Momentum of the System'); xlabel(axes1,'Time (sec)'); ylabel(axes1,'Linear Momentum (kg m/s)'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best');

%Angular Momentum %___________________________________________________ %CREATEFIGURE(X1,Y1,Y2,Y3,Y4) % X1: vector of x data x1 = t; % Y1: matrix of y data y1 = L; % Y2: matrix of y data y2 = Ldot; % Y3: matrix of y data y3 = T; % Y4: matrix of y data y4 = Ldot-T; %


%% Create figure figure1 = figure; %% Create axes axes1 = axes('Position',[0.13 0.5838 0.3347 0.3412],'Parent',figure1); title(axes1,'Angular Momentum about the Origin'); xlabel(axes1,'Time (s)');

292 ylabel(axes1,'Angular Momentum (kg m^2/s)'); box(axes1,'on'); hold(axes1,'all'); %% Create multiple lines using matrix input to plot plot1 = plot(x1,y1); set(plot1(1),'LineWidth',2); set(plot1(2),'LineWidth',2); set(plot1(3),'LineWidth',2); %% Create legend legend1 = legend(axes1,{'X','Y','Z'},'Location','Best'); %% Create axes axes2 = axes('Position',[0.5703 0.5838 0.3347 0.3412],'Parent',figure1); title(axes2,'Rate of Change of the Angular Momentum about the Origin'); xlabel(axes2,'Time (s)'); ylabel(axes2,'Angular Momentum (kg m^2/s^2)'); box(axes2,'on'); hold(axes2,'all'); %% Create multiple lines using matrix input to plot plot2 = plot(x1,y2); set(plot2(1),'LineWidth',2); set(plot2(2),'LineWidth',2); set(plot2(3),'LineWidth',2); %% Create legend legend2 = legend(axes2,{'X','Y','Z'},'Location','Best'); %% Create axes axes3 = axes('Position',[0.13 0.11 0.3347 0.3412],'Parent',figure1); title(axes3,'Net Torque about the Origin'); xlabel(axes3,'Time (s)'); ylabel(axes3,'Torque (N m)'); box(axes3,'on'); hold(axes3,'all'); %% Create multiple lines using matrix input to plot plot3a = plot(x1,y3); set(plot3a(1),'LineWidth',2); set(plot3a(2),'LineWidth',2); set(plot3a(3),'LineWidth',2); %% Create legend legend3 = legend(axes3,{'X','Y','Z'},'Location','Best'); %% Create axes axes4 = axes('Position',[0.5703 0.11 0.3347 0.3412],'Parent',figure1); title(axes4,'Error (Ldot - T)'); xlabel(axes4,'Time (s)'); ylabel(axes4,'Torque (N m)'); box(axes4,'on'); hold(axes4,'all');

293

%% Create multiple lines using matrix input to plot plot4 = plot(x1,y4); set(plot4(1),'LineWidth',2); set(plot4(2),'LineWidth',2); set(plot4(3),'LineWidth',2); %% Create legend legend4 = legend(axes4,{'X','Y','Z'},'Location','Best');

294

Appendix C – Main Routines for Cases 1 and 2 This appendix contains the main routines of the linked simulations in chapter 4. These simulations use the same files shown in Appendix II but link multiple simulations together. Only the main routines are presented for brevity.

Case 1 – Main.m %Main routine for Case 1 linking 3 simulations together % Initialization %___________________________________________________________ clear %Start Time START = datestr(now,13) %Set up the initial conditions IC1 = ICS; %Declare the time variables ti0= 0; %Start Time ti1= 5; %First finish Time ti2= 10; %Second finish Time ti3= 20; %Third Finish Time %First Integration routine %___________________________________________________________ %Integration - results are t1,s1 [t1,s1]=ode45(@SYS1,[ti0,ti1],IC1); FINISH1 = datestr(now,13) %Second Integration routine %__________________________________________________________ %size of s1 [m1,n1] = size(s1); %Set up the initial condition vector as the last row of s1 IC2 = s1(m1,:); %Second integration routine - results are t2, s2 [t2,s2]=ode45(@SYS2,[ti1,ti2],IC2);

295 FINISH2 = datestr(now,13) %Third Integration routine %__________________________________________________________ %size of s2 [m2,n2] = size(s2); %Set up the initial condition vector IC3 = s2(m2,:); %Third integration routine - results are t3, s3 [t3,s3]=ode45(@SYS3,[ti2,ti3],IC3); FINISH3 = datestr(now,13) %Combine the data %____________________________________________________________ %Size of s3 [m3,n3] = size(s3); %Combine the three sets of data t = [t1;t2;t3]; s = [s1;s2;s3]; %Data Manipulation %____________________________________________________________ %Position And Velocity of Rods [X,V,JOINT] = COM (s,m1,m2);

- COM.m

%2nd Derivatives - TT.m [A] = TT (s,m1,m2); %Body Angular Velocities [w1, w2, w3] = Omega (s);

-

Omega.m

%Momentum - Momentum.m [P, L, T, Ldot] = Momentum(s,A,m1,m2); %Joint Angles , Cross Products, Torques [JA1,JA2, CR1, CR2, T1, T3] = Controls (s,m1,m2); %Plots - Plots.m - MatLab Generates this one %___________________________________________________________ Plots(X,s,V,t,w1,w2,w3,P,L,Ldot,T,JA1,JA2,CR1,CR2,T1,T3) %Finish Time FINISH = datestr(now,13)

296

Case 2 – Main.m %Main routine for Case 1 linking 3 simulations together % Initialization %___________________________________________________________ clear %Start Time START = datestr(now,13) %Set up the initial conditions IC1 = ICS; %Declare ti0= 0; ti1= 5; ti2= 20;

the time variables %Start Time %First finish Time %Second finish Time

%First Integration routine %___________________________________________________________ %Integration - results are t1,s1 [t1,s1]=ode45(@SYS1,[ti0,ti1],IC1); FINISH1 = datestr(now,13) %Second Integration routine %__________________________________________________________

%size of s1 [m1,n1] = size(s1); %Set up the initial condition vector as the last row of s1 IC2 = s1(m1,:); %Second Integration routine [t2,s2]=ode45(@SYS2,[ti1,ti2],IC2); %size of s2 [m2,n2] = size(s2); FINISH2 = datestr(now,13) %Combine the two sets of data t = [t1;t2]; s = [s1;s2]; %Data Manipulation

297 %____________________________________________________________ %Position And Velocity of Rods [X,V,JOINT] = COM (s,m1); %2nd Derivatives [A] = TT (s,m1);

- COM.m

- TT.m

%Body Angular Velocities [w1, w2, w3] = Omega (s);

-

Omega.m

%Momentum - Momentum.m [P, L, T, Ldot] = Momentum(s,A,m1); %Joint Angles , Cross Products, Torques [JA1,JA2, CR1, CR2, T1, T3] = Controls (s,m1); %Plots - Plots.m - MatLab Generates this one %___________________________________________________________ Plots(X,s,V,t,w1,w2,w3,P,L,Ldot,T,JA1,JA2,CR1,CR2,T1,T3) %Finish Time FINISH = datestr(now,13)

298

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Hiley, M., Yeadon, M. R., “Maximal dismounts from high bar” J Biomechanics 38 2221-2227 (2005)

3

Atha, J., Hales, F. D., Yeadon, M. R. “The simulation of aerial movement – IV. A computer simulation model” J Biomechanics 23 85-89 (1990) 4

King, M. A., Yeadon, M. R. “A comparison of activation timing profiles for single and double layout somersaults” J Biomechanics 39 s184 (2006) 5

King, M. A., Yeadon, M. R., Wilson, C. “ Modeling the maximum voluntary joint torque/angular velocity relationship in human movement” J Biomechanics 39 476-482 (2006)

6

King, M. A., Kong, P. W., Yeadon, M. R. “Determining subject specific torque parameters from movement data” J Biomechanics 40 s319 (2007) 7

Yeadon, M. R. “The simulation of aerial movement – I. The determination of orientation angles from film data” J Biomechanics 23 59-66 (1990)

8

Yeadon, M. R. “The simulation of aerial movement – II. A mathematical inertia model of the human body” J Biomechanics 23 67-74 (1990) 9

Yeadon, M. R. “The simulation of aerial movement – III. The determination of the angular momentum of the human body” J Biomechanics 23 75-83 (1990) 10

Atha, J., Hales, F. D., Yeadon, M. R. “The simulation of aerial movement – IV. A computer simulation model” J Biomechanics 23 85-89 (1990)

11

Cheng, K. B, Hubbard, M. “Optimal compliant-surface jumping: A multi-segment model of springboard standing jumps” J Biomechanics 38 1822-1829 (2005)

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Blajer, W., Czaplick, A. “Modeling and inverse simulation of somersaults on the trampoline” J Biomechanics 34 1619-1629 (2005)

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Mathiyakom, W., McNitt-Gray, J.L., Wilcox, R. “Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks” J Biomechanics 39 990-1000 (2006)

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Griffiths, I. W., Shapre, D., Watkins, J. “Measuring the moment of inertia of the human body by a rotating platform method” Am. J Physics 73 85-94 (2005)

15

Sprigings, E. J., Yeadon, M. R., “An insight into the reversal of rotation in the Hecht vault” Human Movement Science 16 517-532 (1997)

16

Frohlich, C. “Do springboard divers violate angular momentum conservation?” Am. J Physics 47 583 (1979)

17

18

Edwards, M. H. “Zero angular momentum turns” Am. J Physics 54 846-847 (1986)

Iwai, T. “Geometric mechanics of many-body systems” J Computational and Applied Mathematics 140 403-422 (2002)

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Edwards, M. H. “Zero angular momentum turns” Am. J Physics 54 846-847 (1986)

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Hodgins, J., Wooten, W. L. “Animation of Human Diving” The Eurographics Association (1996)

21

Kane, T. R., Levinson, D. A. “The use of Kane’s dynamical equations in robotics” Intl J Robotics Research 2 3-21 (1983)

22

Ren, G. Zheng, Z. “A quasi-decoupling approach for nonclassical linear systems in state space” J Applied Mechanics 64 946-950 (1997) 23

Costello, M., Frost, G., “Control authority of a projectile equipped with an internal unbalanced part” J Dynamic Systems, Measurement, and Control 128 1005-1012 (2006)

24

Gans, R. F. “On the dynamics of a conservative elastic pendulum” J Applied Mechanics 59 425-430 (1992) 25

Edelstein E., Rosen, A. “Nonlinear dynamics of a flexible multirod (multibeam) system” J Dynamic Systems, Measurement, and Control 120 224-231 (1998)

26

27

Meirovitch, L. Methods of Analytical Dynamics p141 McGraw-Hill (1970) ibid. p142

28

Goldstein H., Poole, C., Safko, J. Classical Mechanics chapter 1 Addison-Wesley (2002)

29

USA DIVING © http://www.usadiving.org/05redesign/media/types_of_dives.htm (09/12/2008)

30

U. S. Parachute Association http://www.uspa.org/AboutSkydiving/FrequentlyAskedQuestions/tabid/57/Default.aspx (11/17/08) 31

King, M. A., Yeadon, M. R., Wilson, C. “ Modeling the maximum voluntary joint torque/angular velocity relationship in human movement” J Biomechanics 39 476-482 (2006)

32

Yeadon, M. R. “The simulation of aerial movement – II. A mathematical inertia model of the human body” J Biomechanics 23 67-74 (1990)

33

Ng, T.C.T., Leung, F.H.F, Tam, P.K.S. “A simple gain scheduled PID control with stability consideration based on a grid-point concept” Proc of the IEE International Symposium on Industrial Electronics 1-3 1090-1094 (1997)