Free vibration of the nonlinear pendulum using hybrid Laplace Adomian decomposition method

Abstract

The pendulum system is definitely nonlinear in the real world of physics and has been considered a fundamental subject to the nonlinear oscillators. In this paper, a hybrid method of the Laplace Adomian decomposition method combined with Padé approximant, named the LADM-Padé approximant technique is proposed to solve the nonlinear undamped and damped pendulum systems to demonstrate efficient and reliable results without small angular displacement assumption or linearization. Three examples here in are given to show the accuracy and convergence in comparison with the fourth-order Runge–Kutta solutions. Copyright © 2009 John Wiley & Sons, Ltd.