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