Exact analytic solutions for the damped Duffing nonlinear oscillator

Panayotounakos, DE; Theotokoglou, EE; Markakis, MP

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Theotokoglou, EE	en
dc.contributor.author	Markakis, MP	en
dc.date.accessioned	2014-03-01T01:24:22Z
dc.date.available	2014-03-01T01:24:22Z
dc.date.issued	2006	en
dc.identifier.issn	1631-0721	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17234
dc.subject	Abel's equation	en
dc.subject	Analytical mechanics	en
dc.subject	Damped Duffing nonlinear oscillator	en
dc.subject.classification	Mechanics	en
dc.subject.other	Damping	en
dc.subject.other	Mathematical models	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Oscillators (mechanical)	en
dc.subject.other	analytical method	en
dc.subject.other	numerical method	en
dc.title	Exact analytic solutions for the damped Duffing nonlinear oscillator	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.crme.2006.03.009	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.crme.2006.03.009	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We prove that the second-order damped nonlinear Duffing oscillator is reduced to an equivalent equation of the normal Abel form of the second kind. Based on a recently developed mathematical methodology for the construction of exact analytic solutions of Abel's equation, exact analytic solutions are obtained for the nonlinear damped Duffing oscillator obeying the initial conditions adapted to the physical problem. To improve the general developed methodology an application concerning the nonlinear Van der Pol free oscillator is briefly discussed. To cite this article: D.E. Panayotounakos et al., C. R. Mecanique 334 (2006). © 2006 Académie des sciences.	en
heal.publisher	ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER	en
heal.journalName	Comptes Rendus - Mecanique	en
dc.identifier.doi	10.1016/j.crme.2006.03.009	en
dc.identifier.isi	ISI:000237937200006	en
dc.identifier.volume	334	en
dc.identifier.issue	5	en
dc.identifier.spage	311	en
dc.identifier.epage	316	en