HAM-based package NOPH for periodic oscillations of nonlinear dynamic systems

Based on Wu's elimination method and the homotopy analysis method (HAM), the Maple package NOPH (version 1.0.2) is developed for periodically oscillating systems of center and limit cycle types, which delivers accurate approximations of frequency, mean of motion and amplitudes of oscillation automatically. Since the HAM is valid for highly nonlinear problems, the package can be used to find accurate approximate solutions of nonlinear oscillation systems with strong nonlinearity. For systems with physical parameters, it can provide possible constraint conditions on parameters. In this chapter, we briefly describe the discussed problem, an efficient algorithm, a Maple package NOPH and so on. A simple users guide is given in the appendix of this chapter. The Maple package NOPH is free available (Accessed 20 Jan 2013, will be updated in the future) at http://numericaltank.sjtu.edu.cn/NOPH.htm.