两自由度机械臂λ^2=1下的Hopf分岔与混沌研究  

Hopf Bifurcation for λ~2=1 and Chaos of a Two-Degree-of-Freedom Manipulator

作　　者：郑小武[1] 

机构地区：[1]西南交通大学,成都610031

出　　处：《应用力学学报》2008年第2期312-315,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10772151);西南交通大学青年教师科研起步项目(2007Q142);西南交通大学基础科学研究基金(2006B08)

摘　　要：研究了一类周期系数力学系统因周期运动失稳而产生Hopf分岔及混沌问题。首先根据拉格朗日方程给出了该力学系统的运动微分方程,并确定其周期运动的具有周期系数的扰动运动微分方程,再根据Floquet理论建立了其给定周期运动的Poincar啨映射,根据该系统的特征矩阵有一对复共轭特征值从-1处穿越单位圆情况,分析该Poincar啨映射不动点失稳后将发生次谐分岔、Hopf分岔、倍周期分岔,而多次倍周期分岔将导致混沌。并用数值计算加以验证。结果表明,随着分岔参数的变化,系统的周期运动可通过次谐分岔形成周期2运动,进而发生Hopf分岔形成拟周期运动,并再次经次谐分岔、倍周期分岔形成混沌运动。The Hopf bifurcation and chaos of a mechanical system with periodic coefficients are investigated while its periodic motion is losing stability. The differential motion equations are given with Lagrange equations, and the perturbed differential equations with periodic coefficients are derived. The Poincar map of the period motion is established following the Floquet theory . Furthermore, the probability of the subharmonic bifurcation, Hopf bifurcation and periodic-doubling bifurcation generation is analyzed according to the eigen-matrix with a pair of Eigenvalues crossing the unit circle from -1. The numerical simulation results reveal that while the parameter changes, the periodic motion may result in period 2 motion via subharmonic bifurcation, or quasi periodic motion via Hopf bifurcation, which leads to chaos motion via subharmonic bifurcation and periodic-doubling bifurcation.

关 键 词：周期系数 力学系统 周期运动 POINCARÉ映射 HOPF分岔 混沌 

分 类 号：O322[理学—一般力学与力学基础]