Rational-harmonic balancing approach to nonlinear phenomena governed by pendulum-like differential equations

Please use this identifier to cite or link to this item: http://hdl.handle.net/10045/12016
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dc.contributorHolografía y Procesado Ópticoen
dc.contributor.authorGimeno, Encarnación-
dc.contributor.authorBeléndez, Augusto-
dc.contributor.otherUniversidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señalen
dc.contributor.otherUniversidad de Alicante. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologíasen
dc.identifier.citationGIMENO NIEVES, Encarnación; BELÉNDEZ VÁZQUEZ, Augusto. "Rational-harmonic balancing approach to nonlinear phenomena governed by pendulum-like differential equations". Zeitschrift für Naturforschung A: Physical Sciences. Vol. 64a, No. 12 (2009). ISSN 0392-0784, pp. 819-826en
dc.description.abstractThis paper presents a new approach for solving accurate approximate analytical solutions for nonlinear phenomena governed by pendulum-like differential equations. The new approach couples Taylor series expansion with rational harmonic balancing. An approximate rational solution depending on a small parameter is considered. After substituting the approximate solution into the governing differential equation, this equation is expanded in Taylor series of the parameter prior to harmonic balancing. The approach gives a cubic equation, which must be solved in order to obtain the value of the small parameter. A method for transforming this cubic equation into a linear equation is presented and discussed. Using this approach, accurate approximate analytical expressions for period and periodic solutions are obtained. We also compared the Fourier series expansions of the analytical approximate solution and the exact one. This allowed us to compare the coefficients for the different harmonic terms in these solutions. These analytical approximations may be of interest for those researchers working in nonlinear physical phenomena governed by pendulum-like differential equations in fields such as classical mechanics, vibrations, acoustics, electromagnetism, electronics, superconductivity, optics, gravitation, and others.en
dc.description.sponsorshipThis work was supported by the “Generalitat Valenciana” of Spain under project ACOMP/2009/150 and by the “Vicerrectorado de Tecnologa e Innovación Educativa” of the University of Alicante, Spain (GITE-09006-UA).en
dc.publisherVerlag der Zeitschrift für Naturforschungen
dc.subjectNonlinear oscillatoren
dc.subjectApproximate solutionsen
dc.subjectRational harmonic balance methoden
dc.subjectNonlinear pendulumen
dc.subject.otherFísica Aplicadaen
dc.titleRational-harmonic balancing approach to nonlinear phenomena governed by pendulum-like differential equationsen
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