物理学报Issue(6)：1-8,8.DOI:10.7498/aps.64.064501
基于Coulomb摩擦效应的一类非线性相对转动系统的混沌研究∗
Chaos of a kind of nonlinear relative rotation system based on the effect of Coulomb friction
摘要
Abstract
Chaotic motion of a kind of nonlinear relative rotation system with load Coulomb frictional damping is investigated. Based on the Lagrange equation of a dissipative system, the dynamic equation of a kind of nonlinear relative rotation system with two pieces of mass is established, which contains a kind of nonlinear load Coulomb frictional damping. The eigenvalue of the autonomous system is discussed using Cardano formula. On this basis, the existence of homoclinic orbits is given by the undetermined coefficient method, and the chaotic motion of the system is investigated by means of Silnikov theorem. Finally the chaotic motion of the system with the known parameters is studied numerically. With the variation of Coulomb frictional damping, a route to chaos through period-doubling bifurcations is exhibited. Numerical calculation can confirm the validity of the analytical results.关键词
相对转动系统/混沌/Coulomb摩擦/同宿轨道Key words
relative rotation system/chaos/Coulomb friction/homoclinic orbit引用本文复制引用
刘爽,田松涛,王振臣,李建雄..基于Coulomb摩擦效应的一类非线性相对转动系统的混沌研究∗[J].物理学报,2015,(6):1-8,8.基金项目
国家自然科学基金(批准号:61104040)、河北省自然科学基金(批准号：E2012203090)和河北省高等学校创新团队领军人才培育计划项目(批准号：LJRC013)资助的课题.* Project supported by the National Natural Science Foundation of China (Grant No.61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013) （批准号:61104040）
