A new method to determine the periodic orbit of a nonlinear dynamic system and its period

Periodic motion is an important steady-state motion in the real world. In this paper, a new generalized shooting method for determining the periodic orbit of a nonlinear dynamic system and its period is presented by rebuilding the traditional shooting method. First, by changing the time scale, the period of the periodic orbit of a nonlinear system is drawn into the governing equation of this system explicitly. Then, the period is used as a parameter in the iteration procedure of the shooting method. The periodic orbit of the system and the period can be determined rapidly and precisely. The requirement of this method for the initial iteration conditions is not rigorous. This method can be used to analyze the forced nonlinear system and the parameter exciting system. As an example, the results of the Rössler equation for an eight-dimensional, nonlinear, flexible, rotor-bearing system are compared with those obtained by the Runge-Kutta integration algorithm. The validity of this method is verified by the numerical results obtained in the two examples.