Beléndez, Augusto, Hernández Prados, Antonio, Beléndez, Tarsicio, Neipp, Cristian, Márquez, Andrés
Application of homotopy perturbation method to the nonlinear pendulum
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
URI: http://hdl.handle.net/10045/2510
DOI: 10.1088/0143-0807/28/1/010
ISSN: 0143-0807
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.
Keywords:Nonlinear oscillator, Approximate solutions, Homotopy perturbation method, Nonlinear pendulum
Institute of Physics Publishing
info:eu-repo/semantics/article