| 广义Hamilton系统的研究概况 |
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| 引用本文： | 赵晓华 程耀. 广义Hamilton系统的研究概况[J]. 力学进展, 1994, 24(3): 289-300. DOI: 10.6052/1000-0992-1994-3-J1994-028 |
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| 作者姓名： | 赵晓华 程耀 |
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| 作者单位： | 云南省应用数学研究所; 云南大学数学系 |
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| 基金项目： | 国家自然科学基金，航空科学基金，国家教委基金和云南省科委基金 |
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| 摘 要： | 用广义Ｐｏｉｓｓｏｎ括号直接定义的广义Ｈａｍｉｌｔｏｎ系统是经典Ｈａｍｉｌｔｏｎ系统的一种推广。由于它的维数没有限制，同时它又保持了经典Ｈａｍｉｌｔｏｎ系统的主要性质，因此具有更大的普遍性和广泛的应用前景。本文简要介绍了广义Ｈａｍｉｌｔｏｎ系统理论的发展历史、基本概念和研究现状。
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| 关 键 词： | 广义Hamilton系统 Poisson结构 约化 稳定性 扰动 分岔 混沌 积分算法 |
REVIEW ON THE RESEARCHES OFGENERALIZED HAMILTONIAN SYSTEMS |
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| Zhao Xiao-huaInstitute uf Applied Math. of Yunnan Province. and Dept.of Math.,Yunnan University,Kunming,Cheng Yao, Lu Qi-shao, Huang Ke-lei. REVIEW ON THE RESEARCHES OFGENERALIZED HAMILTONIAN SYSTEMS[J]. Advances in Mechanics, 1994, 24(3): 289-300. DOI: 10.6052/1000-0992-1994-3-J1994-028 |
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| Authors: | Zhao Xiao-huaInstitute uf Applied Math. of Yunnan Province. Dept.of Math. Yunnan University Kunming Cheng Yao Lu Qi-shao Huang Ke-lei |
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| Affiliation: | Zhao Xiao-huaInstitute uf Applied Math. of Yunnan Province. and Dept.of Math.,Yunnan University,Kunming,650091Cheng Yao, Lu Qi-shao, Huang Ke-leiDepartment of Applied Mathematics and Physics,Beijing Universityof Aeronautics and Astronautics,Beijing |
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| Abstract: | The generalized Hamiltonian system (GHS), defined directly by thegeneralized Poisson bracket, is a generalization of the traditional Hamiltoniansystem defined on (even dim.) symplectic manifold. The GHS can describe moregeneral dynamical systems including odd- and ∞-dimensional systems, hence thestudy on this type of systems will bc very important in theory and applications.In this paper, we give a review on the researches of generalized Hamiltoniansystems in China and abroad. |
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| Keywords: | generalzzed Hamiltonian Systemi generalized Pozsson bracket reduction stability Perturbation bifurcation chaos integrator |
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