| Título: | Application of homotopy perturbation method to the nonlinear pendulum |
| Autores: |
Beléndez Vázquez, Augusto Hernández Prados, Antonio Beléndez Vázquez, Tarsicio Neipp López, Cristian Márquez Ruiz, Andrés |
| Fecha: |
2007-10-27 2007-10-27 2006-08 2007-01 |
| Publicador: | RUA Docencia |
| Fuente: |
 |
| Tipo: | info:eu-repo/semantics/article |
| Tema: |
Nonlinear oscillator Approximate solutions Homotopy perturbation method Nonlinear pendulum Física Aplicada |
| Descripción: |
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. 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. |
| Idioma: | Inglés |
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