Invariant manifolds, nonclassical normal modes, and proper orthogonal modes in the dynamics of the flexible spherical pendulum

Georgiou, IT; Schwartz, IB

dc.contributor.author	Georgiou, IT	en
dc.contributor.author	Schwartz, IB	en
dc.date.accessioned	2014-03-01T01:51:09Z
dc.date.available	2014-03-01T01:51:09Z
dc.date.issued	2001	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/26241
dc.subject	coupled flexible-body/rigid-body dynamics	en
dc.subject	reduced slow dynamics	en
dc.subject	invariant manifolds	en
dc.subject	nonlinear normal modes	en
dc.subject	proper orthogonal modes	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	SLOW	en
dc.subject.other	SYSTEM	en
dc.subject.other	CHAOS	en
dc.subject.other	OSCILLATOR	en
dc.title	Invariant manifolds, nonclassical normal modes, and proper orthogonal modes in the dynamics of the flexible spherical pendulum	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	It is shown that the flexible spherical pendulum undergoes purely slow motions with master and slaved components. The family of slow motions is realized as a three-dimensional invariant manifold in phase space. This manifold is computed analytically by applying the method of geometric singular perturbations. This manifold is nonlinear and for all energy and angular momentum levels is characterized precisely by three PO (proper orthogonal) modes. Its submanifold of zero angular momentum is a two-dimensional invariant manifold; it is the geometric realization of a nonclassical nonlinear normal mode. This normal mode is characterized precisely by two PO modes. The slaved slow dynamics are characterized precisely by a single PO mode. The stability of the slow invariant manifold as well as interactions between fast and slow dynamics are considered.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	NONLINEAR DYNAMICS	en
dc.identifier.isi	ISI:000172384000002	en
dc.identifier.volume	25	en
dc.identifier.issue	1-3	en
dc.identifier.spage	3	en
dc.identifier.epage	31	en