Rigid Body Dynamics

Alexey Borisov, Ivan S. Mamaev

• Publisher: De Gruyter
• Year: 2018
• Print ISBN: 9783110542790
• eBook ISBN: 9783110542974
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Applied Mathematics

This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics.

Contents
Rigid Body Equations of Motion and Their Integration
The Euler – Poisson Equations and Their Generalizations
The Kirchhoff Equations and Related Problems of Rigid Body Dynamics
Linear Integrals and Reduction
Generalizations of Integrability Cases. Explicit Integration
Periodic Solutions, Nonintegrability, and Transition to Chaos
Appendix A: Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations
Appendix B: The Lie Algebra e (4) and Its Orbits
Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top
Appendix D: The Hess Case and Quantization of the Rotation Number
Appendix E: Ferromagnetic Dynamics in a Magnetic Field
Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem
Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids
Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• Introduction
• The Creators of Rigid Body Dynamics
• 1 Rigid Body Equations of Motion and Their Integration
• 2 The Euler – Poisson Equations and Their Generalizations
• 3 The Kirchhoff Equations and Related Problems of Rigid Body Dynamics
• 4 Linear Integrals and Reduction
• 5 Generalizations of Integrability Cases. Explicit Integration
• 6 Periodic Solutions, Nonintegrability, and Transition to Chaos
• A Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations
• B The Lie Algebra e(4) and Its Orbits
• C Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top
• D The Hess Case and Quantization of the Rotation Number
• E Ferromagnetic Dynamics in a Magnetic Field
• F The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem
• G Dynamics of Tops and Material Points on Spheres and Ellipsoids
• H On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
• I The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids
• Bibliography
• Index of Names
• Index