An almost Poisson structure for the generalized rigid body equations

被引：0

作者：

Bloch, AM ^{[1
]}

Crouch, PE ^{[1
]}

Marsden, JE ^{[1
]}

Ratiu, TS ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

LAGRANGIAN AND HAMILTONIAN METHODS FOR NONLINEAR CONTROL | 2000年

关键词：

almost Poisson structure; Poisson Lie groups; Sklyanin bracket; reduction; the rigid body; integrable system;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we introduce almost Poisson structures on Lie groups which generalize Poisson structures based on the use of the classical Yang-Baxter identity. Almost Poisson structures fail to be Poisson structures in the sense that they do not satisfy the Jacobi identity. In the case of cross products of Lie groups, we show that an almost Poisson structure can be used to derive a system which is intimately related to a fundamental Hamiltonian integrable system - the generalized rigid body equations. Copyright (C) 2000 IFAC.

引用

页码：87 / 92

页数：6

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