Rigid body dynamics

✍ Scribed by Alexey V. Borisov, Ivan S. Mamaev

• Publisher: Higher Education Press and Walter de Gruyter
• Year: 2019
• Tongue: English
• Leaves: 531
• Category: Library

✦ Synopsis

Systematic presentation of rigid body dynamics, covering both classical and recent results
Includes extensive illustrations to facilitate understanding
Of interest to applied mathematicians and physicists as well as to engineers.

Aims and Scope:

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.

✦ Table of Contents

Contents......Page 6
Introduction......Page 10
The Creators of Rigid Body Dynamics......Page 18
1. Rigid Body Equations of Motion and Their Integration......Page 25
2. The Euler – Poisson Equations and Their Generalizations......Page 80
3. The Kirchhoff Equations and Related Problems of Rigid Body Dynamics......Page 166
4. Linear Integrals and Reduction......Page 226
5. Generalizations of Integrability Cases. Explicit Integration......Page 250
6. Periodic Solutions, Nonintegrability, and Transition to Chaos......Page 285
A. Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations......Page 380
B. The Lie Algebra e(4) and Its Orbits......Page 396
C. Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top......Page 399
D. The Hess Case and Quantization of the Rotation Number......Page 403
E. Ferromagnetic Dynamics in a Magnetic Field......Page 421
F. The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem......Page 424
G. Dynamics of Tops and Material Points on Spheres and Ellipsoids......Page 429
H. On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation......Page 440
I. The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids......Page 451
Bibliography......Page 492
Index of Names......Page 520
Index......Page 524