不变子流形和非线性自治系统的模态

赵国景; 魏建国

不变子流形和非线性自治系统的模态

赵国景^1,2,
魏建国^1,2

1.
中国矿业大学北京研究生部, 北京 100083;
2.
河北农业大学城建学院, 河北保定 071001

详细信息

中图分类号: O189
计量
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- 被引次数: 0
出版历程
- 收稿日期: 1997-02-17
- 刊出日期: 1998-07-15

Invariant Sub-Manifolds and Modes of Nonlinear Autonomous Systems

Zhao Guojing^1,2,
Wei Jianguo^1,2

1.
Peking Graduate School, China University of Mining and Technology, Beijing 100083. P. R. China;
2.
College of Urban and Rural Construction, Agricultural University of Hebei, Baoding 071001, P. R. China

摘要

摘要: 本文就弱非线性自治系统,引入了不变流形理论的几何描述,应用稳定流形定理,Lyapunov子中心流形定理以及中心流形定理,给出了非线性模态的定义,存在条件以及模态的轨道特性.采用了近似的级数展开方法确定模态子流形及模态运动.给出的算例是对本文方法的验证和解释.
- 非线性 /
- 模态 /
- 不变子流形
Abstract: A definition of the modes of a nonlinear autonomous system was developed.The existence conditions and orbits' nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem,center maifold theorm and sub-center manifold theorem.The Taylor series exyansion was used inorder to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds.Two examples were given to demonstrate the applications.
- invariant manifold /
- mode /
- nonlinear system

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参考文献(13)

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