Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
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http://hdl.handle.net/10045/9206
Títol: | Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method |
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Autors: | Beléndez, Augusto | Pascual, Carolina | Alvarez, Mariela L. | Méndez Alcaraz, David Israel | Yebra Calleja, María Soledad | Hernández Prados, Antonio |
Grups d'investigació o GITE: | Holografía y Procesado Óptico |
Centre, Departament o Servei: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal |
Paraules clau: | Nonlinear oscillators | Approximate solutions | Simple pendulum | Homotopy perturbation method |
Àrees de coneixement: | Física Aplicada |
Data de creació: | 10-de juliol-2008 |
Data de publicació: | 19-de desembre-2008 |
Editor: | Institute of Physics Publishing |
Citació bibliogràfica: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method". Physica Scripta. Vol. 79, No. 1 (Jan. 2009), 015009 (8pp), ISSN 0031-8949 |
Resum: | A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152°). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient. |
Patrocinadors: | This work was supported by the ‘Generalitat Valenciana’, Spain, under project GVPRE/ 2008/182. |
URI: | http://hdl.handle.net/10045/9206 |
ISSN: | 0031-8949 (Print) | 1402-4896 (Online) |
DOI: | 10.1088/0031-8949/79/01/015009 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Revisió científica: | si |
Apareix a la col·lecció: | INV - GHPO - Artículos de Revistas INV - Acústica Aplicada - Artículos de Revistas INV - GMECA - Artículos de Revistas |
Arxius per aquest ítem:
Arxiu | Descripció | Tamany | Format | |
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PS_vol79_n1_015009_2009.pdf | Versión final (acceso restringido) | 211,2 kB | Adobe PDF | Obrir Sol·licitar una còpia |
PS_vol79_n1_015009_2009pre.pdf | Versión revisada (acceso libre) | 2,92 MB | Adobe PDF | Obrir Vista prèvia |
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