Journal
NONLINEAR DYNAMICS
Volume 25, Issue 1-3, Pages 3-31Publisher
SPRINGER
DOI: 10.1023/A:1012990329884
Keywords
coupled flexible-body/rigid-body dynamics; reduced slow dynamics; invariant manifolds; nonlinear normal modes; proper orthogonal modes
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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.
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