Generalization of the modified Lindstedt-Poincare method for solving some strong nonlinear oscillators

Abstract

The modified Lindstedt-Poincare method has been generalized for solving strongly nonlinear oscillators. The original formula (presented by Cheung et al.) covers a class of nonlinear problems. So, it requires another formula to cover the remaining class. Usually two solutions can be found for all nonlinear oscillators (utilizing the original and proposed formulae), but one of them is suitable only. The new formula has been derived in a similar way of Cheung et al. However, using two simple conversion formulae such approximate solutions can be found easily from the classical Lindstedt-Poincare solution. For some rare nonlinear oscillators it requires their combination. In lack of linear restoring force the original formula (of Cheung et al.) fails. The generalized method also covers it. Keywords: Nonlinear oscillation, Perturbation method, Modified Lindstedt-Poincare method