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

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.