Dynamics of Multibody Systems (eBook)

Prof. Wittenburg was Professor for Mechanics at University of Karlsruhe. He is still active in research and has been invited to give lectures all over the world.

Preface 6
Preface to the Second Edition 6
Preface to the First Edition 7
Contents 10
1 Mathematical Notation 13
2 Rigid Body Kinematics 21
2.1 Generalized Coordinates of Angular Orientation 21
2.2 Kinematics of Continuous Motion 35
2.3 Kinematic Differential Equations 44
3 Basic Principles of Rigid Body Dynamics 49
3.1 Kinetic Energy 49
3.2 Angular Momentum 51
3.3 Properties of Moments and of Products of Inertia 52
3.4 Angular Momentum Theorem 56
3.5 Principle of Virtual Power 59
4 Classical Problems of Rigid Body Mechanics 61
4.1 Unsymmetric Torque-Free Rigid Body 61
4.2 Symmetric Torque-Free Rigid Body 70
4.3 Self-Excited Symmetric Rigid Body 72
4.4 Symmetric Heavy Top 74
4.5 Symmetric Heavy Body in a Cardan Suspension 82
4.6 Gyrostat. General Considerations 84
4.7 Torque-Free Gyrostat 89
5 General Multibody Systems 101
5.1 Definition of Goals 101
5.2 Elements of Multibody Systems 103
5.3 Interconnection Structure of Multibody Systems 106
5.4 Principle of Virtual Power for Multibody Systems 117
5.5 Systems with Tree Structure 121
5.6 Systems with Closed Kinematic Chains 141
5.7 Systems with Spherical Joints 162
5.8 Plane Motion 187
5.9 Linear Vibrations of Chains of Bodies 196
6 Impact Problems in Multibody Systems 204
6.1 Basic Assumptions 205
6.2 Velocity Increments. Impulses 208
6.3 Analogy to the Law of Maxwell and Betti 210
6.4 Constraint Impulses and Impulse Couples in Joints 214
6.5 Chain Colliding with a Point Mass 214
Solutions to Problems 220
References 225
Index 230