Hamiltonian weakly damped autonomous systems exhibiting periodic attractors

Kounadis, AN

dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:24:29Z
dc.date.available	2014-03-01T01:24:29Z
dc.date.issued	2006	en
dc.identifier.issn	0044-2275	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17280
dc.subject	Autonomous	en
dc.subject	Dynamic bifurcations	en
dc.subject	Flutter	en
dc.subject	Hamiltonian systems	en
dc.subject	Jacobian eigenvalues	en
dc.subject	Periodic attractors	en
dc.subject	Weak damping	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	NONCONSERVATIVE SYSTEMS	en
dc.subject.other	DISSIPATIVE SYSTEMS	en
dc.subject.other	CYLINDRICAL-SHELLS	en
dc.subject.other	HOPF BIFURCATIONS	en
dc.subject.other	DIVERGENCE	en
dc.subject.other	STABILITY	en
dc.subject.other	INSTABILITY	en
dc.subject.other	OSCILLATIONS	en
dc.subject.other	DYNAMICS	en
dc.subject.other	FLUTTER	en
dc.title	Hamiltonian weakly damped autonomous systems exhibiting periodic attractors	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00033-005-0014-9	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00033-005-0014-9	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	The dynamic local stability of autonomous Hamiltonian, weakly damped, lumped-mass (discrete) systems is reconsidered. For such potential(conservative) systems conditions for the existence of limit cycles are discussed by studying the effect of the damping matrix on the Jacobian eigenvalues. New findings that contradict existing results are presented. Thus, undamped stable symmetric systems with the inclusion of slight damping may experience: (a) a double zero eigenvalue bifurcation, a degenerate Hopf bifurcation and a generic (usual) Hopf bifurcation, and (b) a limit cycle (dynamic) mode of instability prior to the static (divergence) mode of instability (failure of Zieglers kinetic criterion). A variety of numerical examples verified by a nonlinear analysis confirm the validity of the theoretical findings presented herein. © 2006 Birkhäuser Verlag, Basel.	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Zeitschrift fur Angewandte Mathematik und Physik	en
dc.identifier.doi	10.1007/s00033-005-0014-9	en
dc.identifier.isi	ISI:000235739600008	en
dc.identifier.volume	57	en
dc.identifier.issue	2	en
dc.identifier.spage	324	en
dc.identifier.epage	349	en