**Uh-oh, it looks like your Internet Explorer is out of date.**

For a better shopping experience, please upgrade now.

## Overview

## Related collections and offers

## Product Details

ISBN-13: | 9781107042650 |
---|---|

Publisher: | Cambridge University Press |

Publication date: | 09/02/2013 |

Edition description: | 4th Revised ed. |

Pages: | 393 |

Product dimensions: | 7.00(w) x 10.10(h) x 1.10(d) |

## About the Author

## Table of Contents

Preface ix

1 Introduction 1

1.1 Multibody Systems 1

1.2 Reference Frames 3

1.3 Particle Mechanics 6

1.4 Rigid Body Mechanics 11

1.5 Deformable Bodies 15

1.6 Constrained Motion 18

1.7 Computer Formulation and Coordinate Selection 22

1.8 Objectives and Scope of This Book 25

2 Reference Kinematics 28

2.1 Rotation Matrix 29

2.2 Properties of the Rotation Matrix 35

2.3 Successive Rotations 39

2.4 Velocity Equations 47

2.5 Accelerations and Important Identities 55

2.6 Rodriguez Parameters 59

2.7 Euler Angles 63

2.8 Direction Cosines 68

2.9 The 4 × 4 Transformation Matrix 72

2.10 Relationship between Different Orientation Coordinates 80

Problems 82

3 Analytical Techniques 85

3.1 Generalized Coordinates and Kinematic Constraints 86

3.2 Degrees of Freedom and Generalized Coordinate Partitioning 94

3.3 Virtual Work and Generalized Forces 102

3.4 Lagrangian Dynamics 115

3.5 Application to Rigid Body Dynamics 123

3.6 Calculus of Variations 129

3.7 Euler's Equation in the Case of Several Variables 135

3.8 Equations of Motion of Rigid Body Systems 142

3.9 Newton-Euler Equations 150

3.10 Concluding Remarks 154

Problems 156

4 Mechanics of Deformable Bodies 159

4.1 Kinematics of Deformable Bodies 160

4.2 Strain Components 164

4.3 Physical Interpretation of Strains 168

4.4 Rigid Body Motion 169

4.5 Stress Components 172

4.6 Equations of Equilibrium 175

4.7 Constitutive Equations 178

4.8 Virtual Work of the Elastic Forces 183

Problems 186

5 Floating Frame of Reference Formulation 188

5.1 Kinematic Description 189

5.2 Inertia of Deformable Bodies 200

5.3 Generalized Forces 213

5.4 Kinematic Constraints 219

5.5 Equations of Motion 223

5.6 Coupling between Reference and Elastic Displacements 228

5.7 Application to a Multibody System 231

5.8 Use of Independent Coordinates 241

5.9 Dynamic Equations with Multipliers 244

5.10 Generalized Coordinate Partitioning 248

5.11 Organization of Multibody Computer Programs 251

5.12 Numerical Algorithms 254

Problems 263

6 Finite-Element Formulation 267

6.1 Element Shape Functions 268

6.2 Reference Conditions 276

6.3 Kinetic Energy 278

6.4 Generalized Elastic Forces 287

6.5 Characterization of Planar Elastic Systems 288

6.6 Characterization of Spatial Elastic Systems 294

6.7 Coordinate Reduction 300

6.8 The Floating Frame of Reference and Large Deformation Problem 304

Problems 307

7 The Large Deformation Problem 309

7.1 Background 310

7.2 Absolute Nodal Coordinate Formulation 314

7.3 Formulation of the Stiffness Matrix 318

7.4 Equations of Motion 322

7.5 Relationship to the Floating Frame of Reference Formulation 323

7.6 Coordinate Transformation 325

7.7 Consistent Mass Formulation 328

7.8 The Velocity Transformation Matrix 331

7.9 Lumped Mass Formulation 332

7.10 Extension of the Method 335

7.11 Comparison with Large Rotation Vector Formulation 339

Problems 342

Appendix: Linear Algebra 345

A.1 Matrix Algebra 345

A.2 Eigenvalue Analysis 349

A.3 Vector Spaces 350

A.4 Chain Rule of Differentiation 353

A.5 Principle of Mathematical Induction 354

Problems 355

References 357

Index 369