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·
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 manifold theorem and sub_center manifold theorem. The Taylor series expansion was used in order to approach the sub_manifolds of the modes and obtain the motions of the mods on the manifolds. Two examples ware given to demonstrate the applications.
出处
《应用数学和力学》
CSCD
北大核心
1998年第7期641-647,共7页
Applied Mathematics and Mechanics
