G Dynamics of Tops and Material Points on Spheres and Ellipsoids

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刚体动力学 (英文版) 作者：A. V. Borisov, I. S. Mamaev　　 ISBN：978-7-04-050235-0　出版时间：2018-08-20

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Introduction 1

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

Glossary

Index
- 3 The problem of n Hooke centers on a sphere
- 4 Gaffet system
- 1 Point motion on the sphere and ellipsoid (n = 2, 3). An analogy with top dynamics
- Two-dimensional ellipsoid and sphere (E2; S2) (461). Three-dimensional ellipsoid and sphere (E3; S3) (463)
- 2 Harmonic oscillator on S2 and S3. A generalization of the Neumann and Jacobi problems
- Hooke centers on the sphere (464). Generalization of Neumann problem on S2 (466). Generalization of the Jacobi problem on E2 (467)
- Generalization of the Neumann system to S3 (467). Rational separable potentials (468)

G Dynamics of Tops and Material Points on Spheres and Ellipsoids

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