基于Coulomb摩擦效应的一类非线性相对转动系统的混沌研究

研究一类非线性相对转动系统在负载Coulomb摩擦效应下的混沌运动行为. 根据Lagrange方程建立一类含非线性负载Coulomb摩擦阻尼的两个质量相对转动系统的动力学方程. 利用Cardano公式讨论自治系统的特征值, 在此基础上, 应用待定系数法给出系统同宿轨道的存在性, 并借助Silnikov定理研究了系统的混沌行为. 最后数值模拟了给定参数下系统的混沌运动, 并给出在Coulomb摩擦阻尼变化下系统由周期、倍周期通向混沌的途径, 验证了理论分析的正确性.

Chaos of a kind of nonlinear relative rotation system based on the effect of Coulomb friction

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.