物理学报2012，Vol.61Issue(19)：267-274,8.
一类高维相对转动非线性动力系统的Lyapunov-Schmidt约化与奇异性分析
Lyapunov-Schmidt reduction and singularity analysis of a high-dimensional relative-rotation nonlinear dynamical system
摘要
Abstract
The dimensionality reduction and bifurcation of some high-dimensional relative-rotation nonlinear dynamical system are stud- ied. Considering the nonlinear influence factor of a relative-rotation nonlinear dynamic system, the high-dimensional relative-rotation torsional vibration global dynamical equation is established based on Lagrange equation. The equivalent low-dimensional bifurcation equation, which can reveal the low-dimensional equivalent bifurcation equation between the nonlinear dynamics and parameters, can be obtained by reducing the dimensionality system using the method of Lyapunov-Schmidt reduction. On this basis, the bifurcation characteristic is analyzed by taking universal unfolding on the bifurcation equation through using the singularity theory. The simulation is carded out with actual parameters. The parameter region of torsional vibration and the effect of the parameters on the vibration are discussed.关键词
相对转动/高维系统/LS约化/奇异性Key words
relatively rotation/high-dimensional system/L-S reduction/singularity分类
数理科学引用本文复制引用
时培明,韩东颖,李纪召,蒋金水,刘彬..一类高维相对转动非线性动力系统的Lyapunov-Schmidt约化与奇异性分析[J].物理学报,2012,61(19):267-274,8.基金项目
国家自然科学基金（批准号：51005196）和河北省自然科学基金（批准号：F2010001317）资助的课题. （）
