Computational Dynamics

by Shabana, Ahmed A.

• ISBN13: 9780470686157
• ISBN10: 0470686154
• Edition: 3rd
• Format: Hardcover
• Copyright: 2010-03-01
• Publisher: Wiley

Summary

Computational Dynamics presents an introduction to this advanced topic covering the concepts, definitions and techniques used in multibody dynamics and incorporating essential topics regarding kinematics and dynamics of motion in three dimensions. Shabana uses analytical tools including Lagrangian and Hamiltonian methods as well as NewtonEuler Equations. Computational techniques are stressed throughout to illustrate methods of solutions for authentic engineering problems. Most books treat the subject from the "analytical" point of view; that is, they focus on the techniques for analyzing the problems presented. Shabanas book is one of the few available that target the growing market for books that cover the practical computational methods used to solve "realworld" problems. This makes it of particular interest not only for courses, but also as an excellent reference for professional engineers.

Author Biography

Ahmed Shabana, University of Illinois, USA, is the Richard & Loan Hill Professor of Engineering in the Department of Mechanical Engineering at the University of Illinois at Chicago. He is the author of a number of books, including Dynamics of Multibody Systems, Vibration of Discrete and Continuous Systems, and Theory of Vibration: An Introduction.

Table of Contents

Preface	p. xi
Introduction	p. 1
Computational Dynamics	p. 2
Motion and Constraints	p. 3
Degrees of Freedom	p. 6
Kinematic Analysis	p. 9
Force Analysis	p. 11
Dynamic Equations and Their Different Forms	p. 11
Forward and Inverse Dynamics	p. 13
Planar and Spatial Dynamics	p. 15
Computer and Numerical Methods	p. 16
Organization, Scope, and Notations of the Book	p. 18
Linear Algebra	p. 21
Matrices	p. 22
Matrix Operations	p. 24
Vectors	p. 33
Three-Dimensional Vectors	p. 42
Solution of Algebraic Equations	p. 48
Triangular Factorization	p. 55
QR Decomposition	p. 60
Singular Value Decomposition	p. 74
Problems	p. 82
Kinematics	p. 87
Kinematics of Rigid Bodies	p. 88
Velocity Equations	p. 92
Acceleration Equations	p. 94
Kinematics of a Point Moving on a Rigid Body	p. 95
Constrained Kinematics	p. 97
Classical Kinematic Approach	p. 104
Computational Kinematic Approach	p. 124
Formulation of the Driving Constraints	p. 126
Formulation of the Joint Constraints	p. 128
Computational Methods in Kinematics	p. 141
Computer Implementation	p. 150
Kinematic Modeling and Analysis	p. 161
Concluding Remarks	p. 169
Problems	p. 170
Forms of the Dynamic Equations	p. 177
D'Alembert's Principle	p. 178
D'Alembert's Principle and Newton-Euler Equations	p. 182
Constrained Dynamics	p. 186
Augmented Formulation	p. 190
Lagrange Multipliers	p. 191
Elimination of the Dependent Accelerations	p. 193
Embedding Technique	p. 195
Amalgamated Formulation	p. 197
Open-Chain Systems	p. 197
Closed-Chain Systems	p. 203
Concluding Remarks	p. 209
Problems	p. 209
Virtual Work and Lagrangian Dynamics	p. 211
Virtual Displacements	p. 212
Kinematic Constraints and Coordinate Partitioning	p. 215
Virtual Work	p. 225
Examples of Force Elements	p. 231
Workless Constraints	p. 246
Principle of Virtual Work in Statics	p. 247
Principle of Virtual Work in Dynamics	p. 257
Lagrange's Equation	p. 262
Gibbs-Appel Equation	p. 267
Hamiltonian Formulation	p. 267
Relationship between Virtual Work and Gaussian Elimination	p. 274
Problems	p. 276
Constrained Dynamics	p. 283
Generalized Inertia	p. 284
Mass Matrix and Centrifugal Forces	p. 289
Equations of Motion	p. 294
System of Rigid Bodies	p. 296
Elimination of the Constraint Forces	p. 300
Lagrange Multipliers	p. 309
Constrained Dynamic Equations	p. 317
Joint Reaction Forces	p. 323
Elimination of Lagrange Multipliers	p. 326
State Space Representation	p. 329
Numerical Integration	p. 332
Algorithm and Sparse Matrix Implementation	p. 340
Differential and Algebraic Equations	p. 342
Inverse Dynamics	p. 349
Static Analysis	p. 351
Problems	p. 352
Spatial Dynamics	p. 359
General Displacement	p. 360
Finite Rotations	p. 361
Euler Angles	p. 369
Velocity and Acceleration	p. 371
Generalized Coordinates	p. 376
Generalized Inertia Forces	p. 380
Generalized Applied Forces	p. 392
Dynamic Equations of Motion	p. 401
Constrained Dynamics	p. 405
Formulation of the Joint Constraints	p. 408
Newton-Euler Equations	p. 417
D'Alembert's Principle	p. 418
Linear and Angular Momentum	p. 419
Recursive Methods	p. 422
Problems	p. 438
Special Topics in Dynamics	p. 445
Gyroscopes and Euler Angles	p. 445
Rodriguez Formula	p. 450
Euler Parameters	p. 454
Rodriguez Parameters	p. 456
Quaternions	p. 459
Rigid Body Contact	p. 462
Stability and Eigenvalue Analysis	p. 468
Problems	p. 472
Multibody System Computer Codes	p. 475
Introduction to SAMS/2000	p. 476
Code Structure	p. 478
System Identification and Data Structure	p. 479
Installing the Code and Theoretical Background	p. 481
SAMS/2000 Setup	p. 483
Use of the Code	p. 484
Body Data	p. 486
Constraint Data	p. 492
Performing Simulations	p. 496
Batch Jobs	p. 498
Graphics Control	p. 500
Animation Capabilities	p. 503
General Use of the Input Data Panels	p. 503
Spatial Analysis	p. 506
Special Modules and Features of the Code	p. 509
References	p. 515
Index	p. 521
Table of Contents provided by Ingram. All Rights Reserved.

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