期刊论文详细信息
JOURNAL OF GEOMETRY AND PHYSICS 卷:119
Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle
Article
Wang, Hong1,2 
[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
关键词: Hamilton-Jacobi theorem;    Symplectic form;    Momentum map;    Regular point reduction;    Regular orbit reduction;   
DOI  :  10.1016/j.geomphys.2017.04.011
来源: Elsevier
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【 摘 要 】

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively. (C) 2017 Elsevier B.V. All rights reserved.

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