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The symmetric representation of the rigid body equations and their discretization

Bloch, Anthony M. and Crouch, Peter E. and Marsden, Jerrold E. and Ratiu, Tudor S. (2002) The symmetric representation of the rigid body equations and their discretization. Nonlinearity, 15 (4). pp. 1309-1341. ISSN 0951-7715. http://resolver.caltech.edu/CaltechAUTHORS:BLOnonlin02

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Abstract

This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems. In particular, we present a symmetric representation of the rigid body equations on the Cartesian product SO(n) × SO(n) and study its associated symplectic structure. We describe the relationship of these ideas with the Moser–Veselov theory of discrete integrable systems and with the theory of variational symplectic integrators. Preliminary work on the ideas discussed in this paper may be found in Bloch et al (Bloch AM, Crouch P, Marsden J E and Ratiu T S 1998 Proc. IEEE Conf. on Decision and Control 37 2249–54).


Item Type:Article
Additional Information:© 2002 IOP Publishing Ltd. Received 5 July 2001, in final form 7 May 2002. Published 17 June 2002. Print publication: Issue 4 (July 2002). The authors thank R Brockett for useful discussions on this material. The authors also thank the referees whose suggestions greatly improved the exposition of this paper. AMB’s research was partially supported by the NSF and AFOSR. JEM’s research was partially supported by the California Institute of Technology and NSF-KDI grant ATM-9873133. TSR’s work was supported in part by NSF grant DMS-98-02378 and the Swiss NSF.
Record Number:CaltechAUTHORS:BLOnonlin02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BLOnonlin02
Alternative URL:http://dx.doi.org/10.1088/0951-7715/15/4/316
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:555
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Aug 2005
Last Modified:26 Dec 2012 08:40

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