Notes on ‘Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms’
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Title: | Notes on ‘Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms’ |
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Authors: | Beléndez, Augusto | Arribas Garde, Enrique | Francés, Jorge | 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. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías | Universidad de Castilla-La Mancha. Departamento de Física Aplicada | Universidad de Alicante. Departamento de Óptica, Farmacología y Anatomía. |
Keywords: | Nonlinear oscillators | Approximate solutions | Hamiltonian approach | Harmonic balance method |
Knowledge Area: | Física Aplicada | Matemática Aplicada |
Date Created: | 5-Apr-2011 |
Issue Date: | 16-Jun-2011 |
Publisher: | Elsevier |
Citation: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Notes on ‘Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms’". Mathematical and Computer Modelling. Vol. 54, Issues 11-12 (Dec. 2011). ISSN 0895-7177, pp. 3204-3209 |
Abstract: | In a recent paper [A. Yildirim, Z. Saadatnia, H. Askari, “Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms”, Mathematical and Computer Modelling 54 (2011) 697-703] the so-called Hamiltonian approach (HA) was applied to obtain analytical approximate solutions for conservative nonlinear oscillators with certain elastic terms. In this paper we demonstrate that the approach proposed is equivalent to the well known harmonic balance method (HBM) and that the equations they obtained using the HA can be easily derived from the well known first-order HBM applied to conservative nonlinear oscillators with odd nonlinear elastic terms. This implies that the approximate frequency and periodic solution obtained using the HA with the trial function proposed in that paper are the same as those obtained using the first-order HBM. We think the comments presented here could be useful for people working in approximate analytical methods for nonlinear oscillators and they would have to be taken into account in the developing and application of some approximate techniques. |
Sponsor: | This work was supported by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain (GITE-09006-UA) and by the Generalitat Valenciana, Spain (PROMETEO/2011/021). |
URI: | http://hdl.handle.net/10045/19868 |
ISSN: | 0895-7177 (Print) | 1872-9479 (Online) |
DOI: | 10.1016/j.mcm.2011.06.024 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.mcm.2011.06.024 |
Appears in Collections: | INV - GHPO - Artículos de Revistas GITE - FOT - Artículos de Revistas Docencia - Ingeniería y Arquitectura - Otros INV - Acústica Aplicada - Artículos de Revistas |
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File | Description | Size | Format | |
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MCM_v54_n11-12_p3204_2011_pre.pdf | Versión revisada (acceso libre) | 1,18 MB | Adobe PDF | Open Preview |
MCM_v54_n11-12_p3204_2011.pdf | Versión final (acceso restringido) | 202,28 kB | Adobe PDF | Open Request a copy |
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