Application of homotopy perturbation method to the nonlinear pendulum

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Title: Application of homotopy perturbation method to the nonlinear pendulum
Authors: Beléndez, Augusto | Hernández Prados, Antonio | Beléndez, Tarsicio | Neipp, Cristian | Márquez, Andrés
Research Group/s: Holografía y Procesado Óptico
Center, Department or Service: Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal
Keywords: Nonlinear oscillator | Approximate solutions | Homotopy perturbation method | Nonlinear pendulum
Knowledge Area: Física Aplicada
Date Created: Aug-2006
Issue Date: Jan-2007
Publisher: Institute of Physics Publishing
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Application of homotopy perturbation method to the nonlinear pendulum". European Journal of Physics. 28, No. 1 (Jan. 2007). ISSN 0143-0807, pp. 93-104
Abstract: The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130°. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics, although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
Sponsor: This work was supported by the ‘Ministerio de Educación y Ciencia’, Spain, under project FIS2005-05881-C02-02, and by the ‘Generalitat Valenciana’, Spain, under project ACOMP06/007.
URI: |
ISSN: 0143-0807 | 1361-6404
DOI: 10.1088/0143-0807/28/1/010
Language: eng
Type: info:eu-repo/semantics/article
Rights: Copyright © Institute of Physics and IOP Publishing Limited
Peer Review: si
Appears in Collections:INV - GHPO - Artículos de Revistas
GITE - FOT - Artículos de Revistas

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