Chaotic Motions for a Class of the Compound Pendulum System

The dynamics equation of the compound pendulum system is studied with the Melnikov method. The critical condition of the chaotic motion is discussed and the critical curve of the parameter is drawn. With the Runge-Kutta method, Numerical simulations are given, which verified the analytical results. It is concluded that there exists Smale horseshoe chaos arising from transversal intersections of stable and unstable manifold of the homoclinic orbit. The critical values for chaos first increase and then decrease with the increasing of the driving torque.