Computational Dynamics

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Computational Dynamics, 3rd edition , thoroughly revised and updated, provides logical coverage of both theory and numerical computation techniques for practical applications.

The author introduces students to this advanced topic covering the concepts, definitions and techniques used in multi-body system dynamics including essential coverage of kinematics and dynamics of motion in three dimensions. He uses analytical tools including Lagrangian and Hamiltonian methods as well as Newton-Euler Equations.

An educational version of multibody computer code is now included in this new edition www.wiley.com/go/shabana that can be used for instruction and demonstration of the theories and formulations presented in the book, and a new chapter is included to explain the use of this code in solving practical engineering problems.

Most books treat the subject of dynamics from an analytical point of view, focusing on the techniques for analyzing the problems presented. This book is exceptional in that it covers the practical computational methods used to solve "real-world" problems. This makes it of particular interest not only for senior/ graduate courses in mechanical and aerospace engineering, but also to professional engineers.

  • Modern and focused treatment of the mathematical techniques, physical theories and application of rigid body mechanics that emphasizes the fundamentals of the subject, stresses the importance of computational methods and offers a wide variety of examples.
  • Each chapter features simple examples that show the main ideas and procedures, as well as straightforward problem sets that facilitate learning and help readers build problem-solving skills

Author(s): Ahmed A. Shabana
Edition: 3ed.
Publisher: Wiley
Year: 2010

Language: English
Pages: 545

Computational Dynamics......Page 4
CONTENTS......Page 10
PREFACE......Page 14
1 INTRODUCTION......Page 18
1.1 Computational Dynamics......Page 19
1.2 Motion and Constraints......Page 20
1.3 Degrees of Freedom......Page 23
1.4 Kinematic Analysis......Page 26
1.6 Dynamic Equations and Their Different Forms......Page 28
1.7 Forward and Inverse Dynamics......Page 30
1.8 Planar and Spatial Dynamics......Page 32
1.9 Computer and Numerical Methods......Page 33
1.10 Organization, Scope, and Notations of the Book......Page 35
2 LINEAR ALGEBRA......Page 38
2.1 Matrices......Page 39
2.2 Matrix Operations......Page 41
2.3 Vectors......Page 50
2.4 Three-Dimensional Vectors......Page 59
2.5 Solution of Algebraic Equations......Page 65
2.6 Triangular Factorization......Page 72
*2.7 QR Decomposition......Page 77
*2.8 Singular Value Decomposition......Page 91
Problems......Page 99
3 KINEMATICS......Page 104
3.1 Kinematics of Rigid Bodies......Page 105
3.2 Velocity Equations......Page 109
3.3 Acceleration Equations......Page 111
3.4 Kinematics of a Point Moving on a Rigid Body......Page 112
3.5 Constrained Kinematics......Page 114
3.6 Classical Kinematic Approach......Page 121
3.7 Computational Kinematic Approach......Page 141
3.8 Formulation of the Driving Constraints......Page 143
3.10 Computational Methods in Kinematics......Page 158
3.9 Formulation of the Joint Constraints......Page 145
3.11 Computer Implementation......Page 167
3.12 Kinematic Modeling and Analysis......Page 178
3.13 Concluding Remarks......Page 186
Problems......Page 187
4 FORMS OF THE DYNAMIC EQUATIONS......Page 194
4.1 D’Alembert’s Principle......Page 195
4.2 D’Alembert’s Principle and Newton–Euler Equations......Page 199
4.3 Constrained Dynamics......Page 203
4.4 Augmented Formulation......Page 207
4.5 Lagrange Multipliers......Page 208
4.6 Elimination of the Dependent Accelerations......Page 210
4.7 Embedding Technique......Page 212
4.9 Open-Chain Systems......Page 214
4.10 Closed-Chain Systems......Page 220
Problems......Page 226
5 VIRTUAL WORK AND LAGRANGIAN DYNAMICS......Page 228
5.1 Virtual Displacements......Page 229
5.2 Kinematic Constraints and Coordinate Partitioning......Page 232
5.3 Virtual Work......Page 242
5.4 Examples of Force Elements......Page 248
5.5 Workless Constraints......Page 263
5.6 Principle of Virtual Work in Statics......Page 264
5.7 Principle of Virtual Work in Dynamics......Page 274
5.8 Lagrange’s Equation......Page 279
*5.10 Hamiltonian Formulation......Page 284
5.11 Relationship between Virtual Work and Gaussian Elimination......Page 291
Problems......Page 293
6 CONSTRAINED DYNAMICS......Page 300
6.1 Generalized Inertia......Page 301
6.2 Mass Matrix and Centrifugal Forces......Page 306
6.3 Equations of Motion......Page 311
6.4 System of Rigid Bodies......Page 313
6.5 Elimination of the Constraint Forces......Page 317
6.6 Lagrange Multipliers......Page 326
6.7 Constrained Dynamic Equations......Page 334
6.8 Joint Reaction Forces......Page 340
6.9 Elimination of Lagrange Multipliers......Page 343
6.10 State Space Representation......Page 346
6.11 Numerical Integration......Page 349
6.12 Algorithm and Sparse Matrix Implementation......Page 357
6.13 Differential and Algebraic Equations......Page 359
*6.14 Inverse Dynamics......Page 366
*6.15 Static Analysis......Page 368
Problems......Page 369
7 SPATIAL DYNAMICS......Page 376
7.1 General Displacement......Page 377
7.2 Finite Rotations......Page 378
7.3 Euler Angles......Page 386
7.4 Velocity and Acceleration......Page 388
7.5 Generalized Coordinates......Page 393
7.6 Generalized Inertia Forces......Page 397
7.7 Generalized Applied Forces......Page 409
7.8 Dynamic Equations of Motion......Page 418
7.9 Constrained Dynamics......Page 422
7.10 Formulation of the Joint Constraints......Page 425
7.11 Newton–Euler Equations......Page 434
7.12 D’Alembert’s Principle......Page 435
7.13 Linear and Angular Momentum......Page 436
7.14 Recursive Methods......Page 439
Problems......Page 455
8.1 Gyroscopes and Euler Angles......Page 462
8.2 Rodriguez Formula......Page 467
8.3 Euler Parameters......Page 471
8.4 Rodriguez Parameters......Page 473
8.5 Quaternions......Page 476
8.6 Rigid Body Contact......Page 479
8.7 Stability and Eigenvalue Analysis......Page 485
Problems......Page 489
9 MULTIBODY SYSTEM COMPUTER CODES......Page 492
9.1 Introduction to SAMS/2000......Page 493
9.2 Code Structure......Page 495
9.3 System Identification and Data Structure......Page 496
9.4 Installing the Code and Theoretical Background......Page 498
9.5 SAMS/2000 Setup......Page 500
9.6 Use of the Code......Page 501
9.7 Body Data......Page 503
9.8 Constraint Data......Page 509
9.9 Performing Simulations......Page 513
9.10 Batch Jobs......Page 515
9.11 Graphics Control......Page 517
9.13 General Use of the Input Data Panels......Page 520
9.14 Spatial Analysis......Page 523
9.15 Special Modules and Features of the Code......Page 526
REFERENCES......Page 532
INDEX......Page 538