Generalized Shooting Method for Determining the Periodic Orbit of the Nonlinear Dynamics System
Li Dexin,Xu Jianxue
(School of Architectural Engineering and Mechanics, Xi'an Jiaotong University, Xi'an, 710049)

Abstract: In this paper, a new generalized shooting method for determining the periodic orbit and its period of the nonlinear dynamic system is presented by rebuilding the traditional shooting method. At first, by changing the time scale the period of the periodic orbit of the nonlinear system is drawn into the governing equation of this system explicitly, then, the period as a parameter takes par t into the iteration procedure of the shooting method together. The periodic orb it and its period of the system can be determined rapidly and precisely. The method needn't the rigor of the initial iteration conditions and it can be used for analyzing the forced nonlinear systems and also the parametric excited systems. As an illustrative example, the computation results of Rossler equation and an eight-dimensional nonlinear flex-rotor system are compared with those obtained via the Runge-Kutta integration algorithm. The validity of this method is verified by the results obtained in two examples.
Keywords: periodic solution, shooting method, nonlinear dynamic system, bifurcation, chaos.