Wittenburg Dynamics of Multibody Systems

2. Auflage 2007
ISBN: 978-3-540-73914-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 223 Seiten

Investigations into the dynamics of a system of rigid bodies require the formulation of nonlinear equations of motion, of energy expressions, kinematic relationships, and other quantities. It is common practice to develop these for each system separately and to consider the labor necessary for deriving e.g., equations of motion from Lagrange`s equation, as inevitable.

It is the main purpose of this book to describe in detail a formalism which substantially simplifies these tasks.

The book addresses advanced graduate students and scientists.

Autoren/Hrsg.

Wittenburg, Jens

Inhaltsverzeichnis

1;Preface;6
1.1;Preface to the Second Edition;6
1.2;Preface to the First Edition;7
2;Contents;10
3;1 Mathematical Notation;13
4;2 Rigid Body Kinematics;21
4.1;2.1 Generalized Coordinates of Angular Orientation;21
4.2;2.2 Kinematics of Continuous Motion;35
4.3;2.3 Kinematic Differential Equations;44
5;3 Basic Principles of Rigid Body Dynamics;49
5.1;3.1 Kinetic Energy;49
5.2;3.2 Angular Momentum;51
5.3;3.3 Properties of Moments and of Products of Inertia;52
5.4;3.4 Angular Momentum Theorem;56
5.5;3.5 Principle of Virtual Power;59
6;4 Classical Problems of Rigid Body Mechanics;61
6.1;4.1 Unsymmetric Torque-Free Rigid Body;61
6.2;4.2 Symmetric Torque-Free Rigid Body;70
6.3;4.3 Self-Excited Symmetric Rigid Body;72
6.4;4.4 Symmetric Heavy Top;74
6.5;4.5 Symmetric Heavy Body in a Cardan Suspension;82
6.6;4.6 Gyrostat. General Considerations;84
6.7;4.7 Torque-Free Gyrostat;89
7;5 General Multibody Systems;101
7.1;5.1 Definition of Goals;101
7.2;5.2 Elements of Multibody Systems;103
7.3;5.3 Interconnection Structure of Multibody Systems;106
7.4;5.4 Principle of Virtual Power for Multibody Systems;117
7.5;5.5 Systems with Tree Structure;121
7.6;5.6 Systems with Closed Kinematic Chains;141
7.7;5.7 Systems with Spherical Joints;162
7.8;5.8 Plane Motion;187
7.9;5.9 Linear Vibrations of Chains of Bodies;196
8;6 Impact Problems in Multibody Systems;204
8.1;6.1 Basic Assumptions;205
8.2;6.2 Velocity Increments. Impulses;208
8.3;6.3 Analogy to the Law of Maxwell and Betti;210
8.4;6.4 Constraint Impulses and Impulse Couples in Joints;214
8.5;6.5 Chain Colliding with a Point Mass;214
9;Solutions to Problems;220
10;References;225
11;Index;230