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

• Published in: International journal for numerical methods in biomedical engineering Vol. 27; no. 2; pp. 262 - 272
• Main Authors: Tsai, Pa-Yee, Chen, Cha'o-Kuang
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.02.2011; Wiley
• Subjects: Adomian decomposition method; Approximants; Convergence; Decomposition; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Mathematics; nonlinear pendulum; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Oscillators; Padé approximant; Partial differential equations; Partial differential equations, boundary value problems; Pendulums; Physics; Runge-Kutta method; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Adomian polynomial; Free vibration; Adomian decomposition method; Dynamical system; Runge Kutta method; Non linear system; Non linear oscillator; Vibration damping; Angular displacement; nonlinear pendulum; Pendulum; Padé approximant; Non linear effect; Microdisplacement; Linearization
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.1304

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.