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An almost Poisson structure for the generalized rigid body equations

Bloch, Anthony M. and Crouch, Peter E. and Marsden, Jerrold E. and Ratiu, Tudor S. (2000) An almost Poisson structure for the generalized rigid body equations. In: Lagrangian and Hamiltonian methods for nonlinear control. IFAC Workshop Series. Pergamon , Oxford, pp. 87-92. ISBN 0-08-043658-7.

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In this paper we introduce almost Poisson structures on Lie groups which generalize Poisson structures based on the use of the classical Yang-Baxter identity. Almost Poisson structures fail to be Poisson structures in the sense that they do not satisfy the Jacobi identity.In the case of cross products of Lie groups, we show that an almost Poisson structure can be used to derive a system which is intimately related to a fundamental Hamiltonian integrable system — the generalized rigid body equations.

Item Type:Book Section
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URLURL TypeDescription
Ratiu, Tudor S.0000-0003-1972-5768
Additional Information:© 2000 IFAC. Research partially supported by NSF grant DMS- 9803181, AFOSR grant F49620-96-1-0100, and an NSF group infrastructure grant at the University of Michigan. Work supported in part by NSF grant DMS 91011964 and NATO grant CRG 910926. Research partially supported by the California Institute of Technology and NSF grant DMS-9802106. Work supported in part by NSF grant DMS-98-02378 and the Swiss NSF.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0100
University of Michigan NSF groupUNSPECIFIED
NSFDMS 91011964
NATOCRG 910926
Subject Keywords:almost Poisson structure; Poisson Lie groups; Sklyanin bracket; reduction; the rigid body; integrable system
Series Name:IFAC Workshop Series
Record Number:CaltechAUTHORS:20101007-134653427
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20341
Deposited By: Tony Diaz
Deposited On:22 Nov 2010 23:51
Last Modified:09 Mar 2020 13:19

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