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Hamiltonian structures and stability for rigid bodies with flexible attachments

Krishnaprasad, P. S. and Marsden, J. E. (1987) Hamiltonian structures and stability for rigid bodies with flexible attachments. Archive for Rational Mechanics and Analysis, 98 (1). pp. 71-93. ISSN 0003-9527. doi:10.1007/BF00279963.

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The dynamics of a rigid body with flexible attachments is studied. A general framework for problems of this type is established in the context of Poisson manifolds and reduction. A simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration. Second, the Energy-Casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out. The Poisson structure and stability results take into account vibrations of the string, rotations of the rigid body, their coupling at the point of attachment, and centrifugal and Coriolis forces.

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Additional Information:® Springer-Verlag 1987. Communicated by M. Golubitsky. KRISHNAPRASAD'S work was given partial support by the National Science Foundation under Grant ECS-82-19123. by the Minta Martin Fund for Aeronautical Research, and by the Office of Naval Research under Contract NOOOI4-K-1008; MARSDEN'S by DOE Contract DE-AS03-82ERI2097. We thank GLORIA ALVAREZ-SANCHEZ, DARYL HOLM, TOM HUGHES, TUDOR RATIU, and JUAN SIMO for helpful remarks.
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Minta Martin Fund for Aeronautical ResearchUNSPECIFIED
Office of Naval ResearchN000I4-K-1008
Department of EnergyDE-AS03-82ERI2097
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ID Code:19559
Deposited By: Ruth Sustaita
Deposited On:20 Aug 2010 19:51
Last Modified:08 Nov 2021 23:53

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