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

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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 http://hdl.handle.net/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


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