Application of homotopy perturbation method to the nonlinear pendulum
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Título: | Application of homotopy perturbation method to the nonlinear pendulum |
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Autor/es: | Beléndez, Augusto | Hernández Prados, Antonio | Beléndez, Tarsicio | Neipp, Cristian | Márquez, Andrés |
Grupo/s de investigación o GITE: | Holografía y Procesado Óptico |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal |
Palabras clave: | Nonlinear oscillator | Approximate solutions | Homotopy perturbation method | Nonlinear pendulum |
Área/s de conocimiento: | Física Aplicada |
Fecha de creación: | ago-2006 |
Fecha de publicación: | ene-2007 |
Editor: | Institute of Physics Publishing |
Cita bibliográfica: | 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 |
Resumen: | 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. |
Patrocinador/es: | 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: | http://hdl.handle.net/10045/2510 | http://www.iop.org/EJ/abstract/0143-0807/28/1/010 |
ISSN: | 0143-0807 | 1361-6404 |
DOI: | 10.1088/0143-0807/28/1/010 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | Copyright © Institute of Physics and IOP Publishing Limited |
Revisión científica: | si |
Aparece en las colecciones: | INV - GHPO - Artículos de Revistas GITE - FOT - Artículos de Revistas |
Archivos en este ítem:
Archivo | Descripción | Tamaño | Formato | |
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EJP_pendulum_homotopy_2007.pdf | Versión final (acceso restringido) | 142,86 kB | Adobe PDF | Abrir Solicitar una copia |
230657Rev02Nov06.pdf | Borrador revisado (acceso libre) | 645,58 kB | Adobe PDF | Abrir Vista previa |
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