Cubication of conservative nonlinear oscillators
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Title: | Cubication of conservative nonlinear oscillators |
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Authors: | Beléndez, Augusto | Alvarez, Mariela L. | Fernandez-Varo, Helena | Pascual, Inmaculada |
Research Group/s: | Holografía y Procesado Óptico | GITE - Física, Óptica y Telecomunicaciones |
Center, Department or Service: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Departamento de Óptica, Farmacología y Anatomía |
Keywords: | Nonlinear oscillators | Approximate solutions | Chebyshev polynomials |
Knowledge Area: | Física Aplicada |
Date Created: | 8-May-2009 |
Issue Date: | Sep-2009 |
Publisher: | Institute of Physics Publishing |
Citation: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Cubication of conservative nonlinear oscillators". European Journal of Physics. Vol. 30, No. 5 (Sept. 2009). ISSN 0143-0807, pp. 973-981 |
Abstract: | A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analyzed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analyzed to illustrate the usefulness and effectiveness of this scheme. |
Sponsor: | This work was supported by the ‘Vicerrectorado de Tecnología e Innovación Educativa’ of the University of Alicante, Spain (GITE-09006-UA). |
URI: | http://hdl.handle.net/10045/11283 |
ISSN: | 0143-0807 (Print) | 1361-6404 (Online) |
DOI: | 10.1088/0143-0807/30/5/006 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | Copyright © IOP Publishing Ltd |
Peer Review: | si |
Appears in Collections: | INV - GHPO - Artículos de Revistas GITE - FOT - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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EJP_v30_n5_p973_2009.pdf | Versión final (acceso restringido) | 195,95 kB | Adobe PDF | Open Request a copy |
EJP_v30_n5_p973_2009pre.pdf | Versión revisada (acceso libre) | 2,17 MB | Adobe PDF | Open Preview |
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