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Title: Symbolic modeling of multibody systems / by Jean-Claude Samin and Paul Fisette.
Solid mechanics and its applications ;
Solid mechanics and its applications ;
Author: Samin, Jean-Claude.
Fisette, Paul.
General Notes: Includes bibliographical references (pages 455-462) and index.
I Theory 1 -- 1 Fundamental Mechanics 3 -- 1.1 Mathcmatical background and notations 3 -- 1.1.1 Vectors 3 -- 1.1.2 Tensors 8 -- 1.1.3 Array of vectors 9 -- 1.1.4 Vector pre-product tensor 11 -- 1.1.5 An example: the rotation tensor 12 -- 1.1.6 Transformation matrices 14 -- 1.1.7 Euler's theorem on finite rotations 15 -- 1.1.8 Rotation coordinates 17 -- 1.1.9 Time derivatives of vectors and tensors 21 -- 1.1.10 Angular velocity vector 24 -- 1.2 Rigid body representation 26 -- 1.2.1 Rigid body definition 26 -- 1.2.2 Rigid body kinematics 27 -- 1.2.3 Body center of mass 28 -- 1.2.4 Body linear momentum 29 -- 1.2.5 Body angular momentum 30 -- 1.2.6 Inertia tensor 31 -- 1.2.7 Forces and torques acting on a rigid body 34 -- 1.2.8 Power considerations 37 -- 1.3 Newton-Euler equations 38 -- 2 Dynamics of rigid bodies 43 -- 2.2 Generalized coordinates 43 -- 2.2.1 Generalized coordinates and holonomic constraints 43 -- 2.2.2 Generalized velocities and non-holonomic constraints 49 -- 2.2.3 Degrees of freedom 52 -- 2.3 Newton-Euler procedure 54 -- 2.3.1 The procedure 54 -- 2.3.2 An example 58 -- 2.4 Variational Approach 65 -- 2.4.1 Virtual power principle 65 -- 2.4.2 Generalized forces and Lagrange multipliers 75 -- 2.4.3 Physical interpretation of the Lagrange multipliers 79 -- 2.4.4 An example: a pendulum supported by rollers 81 -- 2.4.5 Application of the Lagrange multiplier technique 84 -- 3 Tree-like multibody structures 89 -- 3.1 Definitions, conventions and hypotheses 89 -- 3.1.2 Topology 92 -- 3.1.3 Kinematics: main definitions 93 -- 3.1.4 Dynamics: main definitions 98 -- 3.1.5 Barycentric quantities 99 -- 3.2 Virtual power principle 101 -- 3.2.2 Kinematics and virtual velocity changes 102 -- 3.2.3 Translational vector equation 103 -- 3.2.4 Rotational vector equation 105 -- 3.2.5 Equations of motion 108 -- 3.2.6 Matrix form of the joint equations 112 -- 3.3 Newton-Euler scheme 114 -- 3.3.2 Forward kinematics 115 -- 3.3.3 Backward dynamics 118 -- 3.4 Newton-Euler scheme with barycentric parameters 121 -- 3.4.2 Inverse Dynamics 122 -- 3.4.3 Recursive direct dynamics 125 -- 4 Complex multibody structures 129 -- 4.1 Closed-loop structures 130 -- 4.1.1 Cut of a body 132 -- 4.1.2 Cut in a ball joint 135 -- 4.1.3 Cut of a connecting rod 136 -- 4.2 User joints/constraints 138 -- 4.2.1 Helicoidal joint 138 -- 4.2.2 Kinematically driven joint 140 -- 4.2.3 Transmission by pulley 141 -- 4.2.4 Gear transmission 142 -- 4.3 Point-to-point links 143 -- 4.4 Sub-system segmentation 146 -- 4.4.1 Equations of motion (without constraints between sub-systems) 148 -- 4.4.2 Equations of motion (with constraints between sub-systems) 150 -- 4.5 Complementary multibody kinematics 154 -- 4.5.1 Loop closure kinematics 154 -- 4.5.2 User joint/constraints and point-to-point links 158 -- 4.6 Numerical aspects 158 -- 4.6.1 Coordinate partitioning 158 -- 4.6.2 Pseudo rotation constraints 162 -- 5 Symbolic generation 169 -- 5.2 Symbolic mathematical expressions 172 -- 5.2.1 Tree representation 172 -- 5.2.2 Expression organization 174 -- 5.3 Computer memory: allocation and freeing 179 -- 5.4 Trigonometric expressions 182 -- 5.4.2 Symbolic process 13 -- 5.4.3 Illustrative examples 187 -- 5.5 Recursive scheme condensation 187 -- 5.5.2 Recursive symbolic computation 188 -- 5.5.3 Elimination process 190 -- 5.5.4 Scheme vectorization 192 -- 5.6 Recursive symbolic differentiation 194 -- 5.6.2 Recursive scheme differentiation 196 -- 5.7 Performance evaluation 198 -- 5.7.2 Performance comparison 198 -- 5.8 Computer implementation 203 -- 5.8.1 Joint modeling hypothesis 203 -- 5.8.2 Program overview 205 -- 5.8.3 Description of the symbolic models 207 -- 5.9 A short example: the four-bar mechanism 209 -- 5.9.1 Symbolic input files 210 -- 5.9.2 Symbolic output files 211 -- II Special topics 217 -- 6 Road vehicles: wheel/ground model 219 -- 6.2 Definitions and hypotheses 220 -- 6.3 Wheel/ground geometrical contact 223 -- 6.3.1 Point and vector definitions 223 -- 6.3.2 Contact point: geometrical solution 225 -- 6.4 Wheel/ground forces and torques 228 -- 6.4.1 Wheel/ground contact kinematics 228 -- 6.4.2 Contact force model 230 -- 6.5 Numerical examples 238 -- 6.5.2 The ILTIS vehicle benchmark 239 -- 6.5.3 An off-road vehicle 244 -- 6.5.4 A complete modern car 245 -- 7 Railway vehicles: wheel/rail model 249 -- 7.2 Wheel/rail kinematic model 251 -- 7.2.1 Contact model of a wheel on a straight track 251 -- 7.2.2 Contact of a wheel on a curved track (with constant radius) 260 -- 7.3 Wheel/rail contact forces and torques 261 -- 7.3.1 Wheel/rail contact kinematics 261 -- 7.3.2 Wheel/rail contact forces 262 -- 7.4 Applications in railway dynamics 263 -- 7.4.1 Geometrical contact between a S1002 wheelset and UIC60 rails 263 -- 7.4.2 Limit cycle of a rigid wheelset at constant speed 265 -- 7.4.3 BAS 2000 bogie 265 -- 7.4.4 Tramway 2000 269 -- 8 Mechanisms: cam/follower model 273 -- 8.2 Description of cam/follower systems 274 -- 8.2.1 Hypotheses and general notations 274 -- 8.2.2 Cam and follower profiles 276 -- 8.3 Kinematic constraints 278 -- 8.3.1 Preliminary computations 278 -- 8.3.2 Contact constraints 280 -- 8.3.3 Constraint derivatives 283 -- 8.4 Contact forces 287 -- 8.4.1 Permanent contact 287 -- 8.4.2 Intermittent contact 291 -- 8.5 Numerical examples 293 -- 8.5.2 Cam/follower model: numerical validation 294 -- 8.5.3 Cam/follower model: experimental validation 294 -- 8.5.4 Modeling of universal wheels 296 -- 9 Multibody systems with flexible beams 301 -- 9.2 The finite segment approach 304 -- 9.3 The assumed mode approach 305 -- 9.3.1 Description of the flexible beam 305 -- 9.3.2 Kinematics 309 -- 9.3.3 Joint equations 315 -- 9.3.4 Deformation equations 321 -- 9.3.5 Symbolic computation of the equations of motion 333 -- 9.4 Numerical examples 336 -- 10 Time integration of flexible MBS 345 -- 10.2 Implicit integration method 347 -- 10.2.1 Residual formulation of the MBS equations in a Newmark scheme 347 -- 10.2.2 Iterative solution of the reduced form 349 -- 10.2.3 Local truncation error estimation 352 -- 10.2.4 Contribution of symbolic generation 352 -- 10.3 General algorithm -- optimization strategy 354 -- 10.3.1 General algorithm 354 -- 10.3.2 Numerical optimization 354 -- 10.4 Numerical Example 357 -- 10.4.1 Validation 358 -- 10.4.2 Evaluation of the proposed method 359 -- III Tutorial 363 -- 11.1 Methodology 366 -- 11.1.1 Analysis 367 -- 11.1.2 Program run 369 -- 11.2 Problem statements 372 -- 11.2.1 Problem 1: a double spring-mass system 372 -- 11.2.2 Problem 2: a merry-go-round 372 -- 11.2.3 Problem 3: a small cart 372 -- 11.2.4 Problem 4: a slider-crank mechanism 372 -- 11.2.5 Problem 5: small cart 2 372 -- 11.2.6 Problem 6: a five-point suspension 372 -- 11.2.7 Problem 7: a jeep suspension 373 -- 11.2.8 Problem 8: a jeep 373 -- 11.2.9 Problem 9: a flexible slider-crank 373 -- 11.2.10 Problem 10: a radiation counter 373 -- 11.2.11 Problem 11: a "cam/follower" device 373 -- 12 Problems 375 -- 12.1 A double spring-mass system 375 -- 12.1.1 Analysis 375 -- 12.1.2 Multibody model 376 -- 12.1.3 Computer pre-process 377 -- 12.1.4 Computer process 378 -- 12.1.5 Computer post-process 379 -- 12.2 A merry-go-round 380 -- 12.2.1 Analysis 380 -- 12.2.2 Multibody model 382 -- 12.2.3 Computer pre-process 383 -- 12.2.4 Computer process 385 -- 12.2.5 Computer post-process 387 -- 12.3 A small cart 388 -- 12.3.1 Analysis 388 -- 12.3.2 Multibody model 389 -- 12.3.3 Computer pre-process 391 -- 12.3.4 Computer process 393 -- 12.3.5 Computer post-process 394 -- 12.4 A slider-crank mechanism 395 -- 12.4.1 Analysis 396 -- 12.4.2 Multibody model 397 -- 12.4.3 Computer pre-process 398 -- 12.4.4 Computer process 399 -- 12.4.5 Computer post-process 400 -- 12.5 Small cart 2 401 -- 12.5.1 Analysis 401 -- 12.5.2 Multibody model 401 -- 12.5.3 Computer pre-process 402 -- 12.5.4 Computer process 403 -- 12.5.5 Computer post-process 403 -- 12.6 A five-point suspension 405 -- 12.6.1 Analysis 405 -- 12.6.2 Multibody model 407 -- 12.6.3 Computer pre-process 408 -- 12.6.4 Computer process 411 -- 12.6.5 Computer post-process 412 -- 12.7 A jeep suspension 415 -- 12.7.1 Analysis 416 -- 12.7.2 Multibody model 418 -- 12.7.3 Computer pre-process 420 -- 12.7.4 Computer process 421 -- 12.7.5 Computer post-process 422 -- 12.8 A jeep 423 -- 12.8.1 Analysis 423 -- 12.8.2 Multibody model 425 -- 12.8.3 Computer pre-process 426 -- 12.8.4 Computer process 429 -- 12.8.5 Computer post-process 431 -- 12.9 A flexible slider-crank 434 -- 12.9.1 Analysis 434 -- 12.9.2 Multibody model 436 -- 12.9.3 Computer pre-process 437 -- 12.9.4 Computer process 437 -- 12.9.5 Computer post-process 439 -- 12.10 A radiation counter 440 -- 12.10.1 Analysis 440 -- 12.10.2 Multibody model 441 -- 12.10.3 Computer pre-process 442 -- 12.10.4 Computer process 444 -- 12.10.5 Computer post-process 446 -- 12.11 A "cam/follower" device 447 -- 12.11.1 Analysis 447 -- 12.11.2 Multibody model 448 -- 12.11.3 Computer pre-process 449 -- 12.11.4 Computer process 450 -- 12.11.5 Computer post-process 452.

Publisher: Kluwer Academic Publishers,
Publication Place: Dordrecht ; Boston :
ISBN: 1402016298 (hbk.)
9781402016295 (hbk.)
Subject: Dynamics -- Computer programs.
Multibody systems.
Series: Solid mechanics and its applications ; v. 112
Solid mechanics and its applications ; v. 112.
Contents: Theory Fundamental Mechanics Mathcmatical background and notations Vectors Tensors Array of vectors Vector pre-product tensor An example: the rotation tensor Transformation matrices Euler's theorem on finite rotations Rotation coordinates Time derivatives of vectors and tensors Angular velocity vector Rigid body representation Rigid body definition Rigid body kinematics Body center of mass Body linear momentum Body angular momentum Inertia tensor Forces and torques acting on a rigid body Power considerations Newton-Euler equations Dynamics of rigid bodies Generalized coordinates Generalized coordinates and holonomic constraints Generalized velocities and non-holonomic constraints Degrees of freedom Newton-Euler procedure The procedure An example Variational Approach Virtual power principle Generalized forces and Lagrange multipliers Physical interpretation of the Lagrange multipliers An example: a pendulum supported by rollers Application of the Lagrange multiplier technique Tree-like multibody structures Definitions, conventions and hypotheses Topology Kinematics: main definitions Dynamics: main definitions Barycentric quantities Virtual power principle Kinematics and virtual velocity changes Translational vector equation Rotational vector equation Equations of motion Matrix form of the joint equations Newton-Euler scheme Forward kinematics Backward dynamics Newton-Euler scheme with barycentric parameters Inverse Dynamics Recursive direct dynamics Complex multibody structures Closed-loop structures Cut of a body Cut in a ball joint Cut of a connecting rod User joints/constraints Helicoidal joint Kinematically driven joint Transmission by pulley Gear transmission Point-to-point links Sub-system segmentation Equations of motion (without constraints between sub-systems) Equations of motion (with constraints between sub-systems) Complementary multibody kinematics Loop closure kinematics User joint/constraints and point-to-point links Numerical aspects Coordinate partitioning Pseudo rotation constraints Symbolic generation Symbolic mathematical expressions Tree representation Expression organization Computer memory: allocation and freeing Trigonometric expressions Symbolic process Illustrative examples Recursive scheme condensation Recursive symbolic computation Elimination process Scheme vectorization Recursive symbolic differentiation Recursive scheme differentiation Performance evaluation Performance comparison Computer implementation Joint modeling hypothesis Program overview Description of the symbolic models A short example: the four-bar mechanism Symbolic input files Symbolic output files Special topics Road vehicles: wheel/ground model Definitions and hypotheses Wheel/ground geometrical contact Point and vector definitions Contact point: geometrical solution Wheel/ground forces and torques Wheel/ground contact kinematics Contact force model Numerical examples The ILTIS vehicle benchmark An off-road vehicle A complete modern car Railway vehicles: wheel/rail model Wheel/rail kinematic model Contact model of a wheel on a straight track Contact of a wheel on a curved track (with constant radius) Wheel/rail contact forces and torques Wheel/rail contact kinematics Wheel/rail contact forces Applications in railway dynamics Geometrical contact between a S1002 wheelset and UIC60 rails Limit cycle of a rigid wheelset at constant speed BAS 2000 bogie Tramway 2000 Mechanisms: cam/follower model Description of cam/follower systems Hypotheses and general notations Cam and follower profiles Kinematic constraints Preliminary computations Contact constraints Constraint derivatives Contact forces Permanent contact Intermittent contact Numerical examples Cam/follower model: numerical validation Cam/follower model: experimental validation Modeling of universal wheels Multibody systems with flexible beams The finite segment approach The assumed mode approach Description of the flexible beam Kinematics Joint equations Deformation equations Symbolic computation of the equations of motion Numerical examples Time integration of flexible MBS Implicit integration method Residual formulation of the MBS equations in a Newmark scheme Iterative solution of the reduced form Local truncation error estimation Contribution of symbolic generation General algorithm -- optimization strategy General algorithm Numerical optimization Numerical Example Validation Evaluation of the proposed method Tutorial Methodology Analysis Program run Problem statements Problem 1: a double spring-mass system Problem 2: a merry-go-round Problem 3: a small cart Problem 4: a slider-crank mechanism Problem 5: small cart 2 Problem 6: a five-point suspension Problem 7: a jeep suspension Problem 8: a jeep Problem 9: a flexible slider-crank Problem 10: a radiation counter Problem 11: a "cam/follower" device Problems A double spring-mass system Analysis Multibody model Computer pre-process Computer process Computer post-process A merry-go-round Analysis Multibody model Computer pre-process Computer process Computer post-process A small cart Analysis Multibody model Computer pre-process Computer process Computer post-process A slider-crank mechanism Analysis Multibody model Computer pre-process Computer process Computer post-process Small cart 2 Analysis Multibody model Computer pre-process Computer process Computer post-process A five-point suspension Analysis Multibody model Computer pre-process Computer process Computer post-process A jeep suspension Analysis Multibody model Computer pre-process Computer process Computer post-process A jeep Analysis Multibody model Computer pre-process Computer process Computer post-process A flexible slider-crank Analysis Multibody model Computer pre-process Computer process Computer post-process A radiation counter Analysis Multibody model Computer pre-process Computer process Computer post-process A "cam/follower" device Analysis Multibody model Computer pre-process Computer process Computer post-process

Physical Description: xi, 469 pages : illustrations ;

Formatted Contents Note: I 1 -- 1 3 -- 1.1 3 -- 1.1.1 3 -- 1.1.2 8 -- 1.1.3 9 -- 1.1.4 11 -- 1.1.5 12 -- 1.1.6 14 -- 1.1.7 15 -- 1.1.8 17 -- 1.1.9 21 -- 1.1.10 24 -- 1.2 26 -- 1.2.1 26 -- 1.2.2 27 -- 1.2.3 28 -- 1.2.4 29 -- 1.2.5 30 -- 1.2.6 31 -- 1.2.7 34 -- 1.2.8 37 -- 1.3 38 -- 2 43 -- 2.2 43 -- 2.2.1 43 -- 2.2.2 49 -- 2.2.3 52 -- 2.3 54 -- 2.3.1 54 -- 2.3.2 58 -- 2.4 65 -- 2.4.1 65 -- 2.4.2 75 -- 2.4.3 79 -- 2.4.4 81 -- 2.4.5 84 -- 3 89 -- 3.1 89 -- 3.1.2 92 -- 3.1.3 93 -- 3.1.4 98 -- 3.1.5 99 -- 3.2 101 -- 3.2.2 102 -- 3.2.3 103 -- 3.2.4 105 -- 3.2.5 108 -- 3.2.6 112 -- 3.3 114 -- 3.3.2 115 -- 3.3.3 118 -- 3.4 121 -- 3.4.2 122 -- 3.4.3 125 -- 4 129 -- 4.1 130 -- 4.1.1 132 -- 4.1.2 135 -- 4.1.3 136 -- 4.2 138 -- 4.2.1 138 -- 4.2.2 140 -- 4.2.3 141 -- 4.2.4 142 -- 4.3 143 -- 4.4 146 -- 4.4.1 148 -- 4.4.2 150 -- 4.5 154 -- 4.5.1 154 -- 4.5.2 158 -- 4.6 158 -- 4.6.1 158 -- 4.6.2 162 -- 5 169 -- 5.2 172 -- 5.2.1 172 -- 5.2.2 174 -- 5.3 179 -- 5.4 182 -- 5.4.2 13 -- 5.4.3 187 -- 5.5 187 -- 5.5.2 188 -- 5.5.3 190 -- 5.5.4 192 -- 5.6 194 -- 5.6.2 196 -- 5.7 198 -- 5.7.2 198 -- 5.8 203 -- 5.8.1 203 -- 5.8.2 205 -- 5.8.3 207 -- 5.9 209 -- 5.9.1 210 -- 5.9.2 211 -- II 217 -- 6 219 -- 6.2 220 -- 6.3 223 -- 6.3.1 223 -- 6.3.2 225 -- 6.4 228 -- 6.4.1 228 -- 6.4.2 230 -- 6.5 238 -- 6.5.2 239 -- 6.5.3 244 -- 6.5.4 245 -- 7 249 -- 7.2 251 -- 7.2.1 251 -- 7.2.2 260 -- 7.3 261 -- 7.3.1 261 -- 7.3.2 262 -- 7.4 263 -- 7.4.1 263 -- 7.4.2 265 -- 7.4.3 265 -- 7.4.4 269 -- 8 273 -- 8.2 274 -- 8.2.1 274 -- 8.2.2 276 -- 8.3 278 -- 8.3.1 278 -- 8.3.2 280 -- 8.3.3 283 -- 8.4 287 -- 8.4.1 287 -- 8.4.2 291 -- 8.5 293 -- 8.5.2 294 -- 8.5.3 294 -- 8.5.4 296 -- 9 301 -- 9.2 304 -- 9.3 305 -- 9.3.1 305 -- 9.3.2 309 -- 9.3.3 315 -- 9.3.4 321 -- 9.3.5 333 -- 9.4 336 -- 10 345 -- 10.2 347 -- 10.2.1 347 -- 10.2.2 349 -- 10.2.3 352 -- 10.2.4 352 -- 10.3 354 -- 10.3.1 354 -- 10.3.2 354 -- 10.4 357 -- 10.4.1 358 -- 10.4.2 359 -- III 363 -- 11.1 366 -- 11.1.1 367 -- 11.1.2 369 -- 11.2 372 -- 11.2.1 372 -- 11.2.2 372 -- 11.2.3 372 -- 11.2.4 372 -- 11.2.5 372 -- 11.2.6 372 -- 11.2.7 373 -- 11.2.8 373 -- 11.2.9 373 -- 11.2.10 373 -- 11.2.11 373 -- 12 375 -- 12.1 375 -- 12.1.1 375 -- 12.1.2 376 -- 12.1.3 377 -- 12.1.4 378 -- 12.1.5 379 -- 12.2 380 -- 12.2.1 380 -- 12.2.2 382 -- 12.2.3 383 -- 12.2.4 385 -- 12.2.5 387 -- 12.3 388 -- 12.3.1 388 -- 12.3.2 389 -- 12.3.3 391 -- 12.3.4 393 -- 12.3.5 394 -- 12.4 395 -- 12.4.1 396 -- 12.4.2 397 -- 12.4.3 398 -- 12.4.4 399 -- 12.4.5 400 -- 12.5 401 -- 12.5.1 401 -- 12.5.2 401 -- 12.5.3 402 -- 12.5.4 403 -- 12.5.5 403 -- 12.6 405 -- 12.6.1 405 -- 12.6.2 407 -- 12.6.3 408 -- 12.6.4 411 -- 12.6.5 412 -- 12.7 415 -- 12.7.1 416 -- 12.7.2 418 -- 12.7.3 420 -- 12.7.4 421 -- 12.7.5 422 -- 12.8 423 -- 12.8.1 423 -- 12.8.2 425 -- 12.8.3 426 -- 12.8.4 429 -- 12.8.5 431 -- 12.9 434 -- 12.9.1 434 -- 12.9.2 436 -- 12.9.3 437 -- 12.9.4 437 -- 12.9.5 439 -- 12.10 440 -- 12.10.1 440 -- 12.10.2 441 -- 12.10.3 442 -- 12.10.4 444 -- 12.10.5 446 -- 12.11 447 -- 12.11.1 447 -- 12.11.2 448 -- 12.11.3 449 -- 12.11.4 450 -- 12.11.5 452.

Electronic Location: http://catdir.loc.gov/catdir/enhancements/fy0823/2003062007-d.html

Publication Date: 2003.

	Agency:	Collection:	Call No.:	Item Type:	Status:	Copy:	Barcode:	Media Type:
	JU Main Library	General	531.11 S188	Normal Circulation	Available	1	JUF0754947	Book