Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
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Title: | Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator |
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Authors: | Beléndez, Augusto | Pascual, Carolina |
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 oscillations | Relativistic oscillator | Harmonic balance method | Approximate frequency |
Knowledge Area: | Física Aplicada |
Date Created: | 22-Aug-2007 |
Issue Date: | 12-Sep-2007 |
Publisher: | Elsevier |
Citation: | BELÉNDEZ VÁZQUEZ, Augusto; PASCUAL VILLALOBOS, Carolina. "Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator". Physics Letters A. Vol. 371, Issue 4 (19 Nov. 2007). ISSN 0375-9601, pp. 291-299 |
Abstract: | The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency–amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%.We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A. |
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 ACOMP/2007/020. |
URI: | http://hdl.handle.net/10045/9135 |
ISSN: | 0375-9601 (Print) | 1873-2429 (Online) |
DOI: | 10.1016/j.physleta.2007.09.010 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.physleta.2007.09.010 |
Appears in Collections: | INV - GHPO - Artículos de Revistas INV - GMECA - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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PLA_v371_n4_p291_2007.pdf | Versión final (acceso restringido) | 226,4 kB | Adobe PDF | Open Request a copy |
PLA_v371_n4_p291_2007pre.pdf | Versión revisada (acceso libre) | 2,64 MB | Adobe PDF | Open Preview |
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