摘要
由H .Poincare和A .M .Lyapunov建立的动力系统的定性理论和稳定性理论是基于相空间的 ,作者通过对系数矩阵A进行变换和分析 ,提出一种在系数空间上研究平面动力系统定性性质和稳定性的几何方法———特征 耦合圆法 ,并用此方法对一简谐系统进行了分析和描述 .结果表明 ,分析动力系统的定性性质和稳定性既可在相空间上进行 ,也可在系数空间上进行 .此外 ,该方法也可推广到非线性系统和高维系统中 。
Qualitative theory and stability theory established by H.Poincare and A.M.Lyapunoy are both based on phase space. By means of transformation and analysis with regard to coefficient matrix A, a method of qualitative analysis and stability analysis of dynamical systems——eigen coupling circle method was put forward in this paper, and a damped harmonic system was analysed using the method, which shows qualitative analysis and stability analysis of dynamical system may be carried out not only in phase space but also in coefficient space. In addition, this method may also be extended to nonlinear system and multidimension system, and some problems difficult to solve in phase space will be easy to solve in coefficient space. [
出处
《中南工业大学学报》
CSCD
北大核心
2000年第1期67-70,共4页
Journal of Central South University of Technology(Natural Science)
基金
国家自然科学基金资助项目 !( 5 983 5 170 )
关键词
动力系统
几何方法
稳定性
定性性质
dynamic system
geometric method
eigen coupling circle
