Invariant Sub-Manifolds and Modes of Nonlinear Autonomous Systems
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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.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.
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Key words:
- invariant manifold /
- mode /
- nonlinear system
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