The U (n) free rigid body: Integrability and stability analysis of the equilibria

被引：5

作者：

Ratiu, Tudor S. ^{[1
]}

Tarama, Daisuke ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland

[2] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 12期

基金：

瑞士国家科学基金会;

关键词：

Free rigid body; Bi-Hamiltonian structure; Integrable system; Equilibrium; Lyapunov stability; HAMILTONIAN-SYSTEMS; SINGULARITIES; INTEGRALS; MANIFOLDS;

D O I：

10.1016/j.jde.2015.08.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A natural extension of the free rigid body dynamics to the unitary group U (n) is considered. The dynamics is described by the Euler equation on the Lie algebra u(n), which has a bi-Hamiltonian structure, and it can be reduced onto the adjoint orbits, as in the case of the SO(n). The complete integrability and the stability of the isolated equilibria on the generic orbits are considered by using the method of Bolsinov and Oshemkov. In particular, it is shown that all the isolated equilibria on generic orbits are Lyapunov stable. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：7284 / 7331

页数：48

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