Comments on “investigation of the properties of the period for the nonlinear oscillator x''+(1+x^2)x'=0”

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Title: Comments on “investigation of the properties of the period for the nonlinear oscillator x''+(1+x^2)x'=0”
Authors: Beléndez, Augusto | Beléndez, Tarsicio | Hernández Prados, Antonio | Gallego, Sergi | Ortuño, Manuel | Neipp, Cristian
Research Group/s: Holografía y Procesado Óptico
Center, Department or Service: Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal
Keywords: Nonlinear oscillator | Approximate solutions | Modified Lindstedt-Poincaré method
Knowledge Area: Física Aplicada
Date Created: 2007
Issue Date: 20-Jun-2007
Publisher: Elsevier
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Comments on “investigation of the properties of the period for the nonlinear oscillator x''+(1+x^2)x'=0". Journal of Sound and Vibration. Vol. 303, Issues 3-5 (20 June 2007). ISSN 0022-460X, pp. 925-930
Abstract: Two Lidstedt-Poincaré perturbation based methods are used to solve the nonlinear differential equation of a nonlinear oscillator having the square of the angular frequency depends quadratically on the velocity. Mickens published two interesting papers [1, 2] about this oscillator and by using the harmonic balance method he found the approximate frequency is not defined for amplitudes of magnitude equal to or larger to two. We show these standard perturbation methods work better than the harmonic balance method. In particular, the modified Lindstedt-Poincaré method works well for the whole range of the oscillation amplitudes, and excellent agreement of the approximate frequency with the exact one has been demonstrated and discussed.
Sponsor: 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 ACOMP006/007.
URI: http://hdl.handle.net/10045/2511
ISSN: 0022-460X
DOI: 10.1016/j.jsv.2007.02.005
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jsv.2007.02.005
Appears in Collections:INV - GHPO - Artículos de Revistas

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