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Dirac structures and the Legendre transformation for implicit Lagrangian and Hamiltonian systems

Yoshimura, Hiroaki and Marsden, Jerrold E. (2007) Dirac structures and the Legendre transformation for implicit Lagrangian and Hamiltonian systems. In: Lagrangian and Hamiltonian methods for nonlinear control 2006: Proceedings from the 3rd IFAC workshop. Lecture Notes in Control and Information. No.366. Berlin : Springer , Nagoya-Japan, pp. 233-247. ISBN 9783540738893.

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This paper begins by recalling how a constraint distribution on a configuration manifold induces a Dirac structure together with an implicit Lagrangian system, a construction that is valid even for degenerate Lagrangians. In such degenerate cases, it is shown in this paper that an implicit Hamiltonian system can be constructed by using a generalized Legendre transformation, where the primary constraints are incorporated into a generalized Hamiltonian on the Pontryagin bundle. Some examples of degenerate Lagrangians for L-C circuits, nonholonomic systems, and point vortices illustrate the theory.

Item Type:Book Section
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Additional Information:© Springer-Verlag Berlin Heidelberg 2007. This research was partially supported by JSPS Grant 16560216 and NSF-ITR Grant ACI-0204932.
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)16560216
Series Name:Lecture Notes in Control and Information
Issue or Number:366
Record Number:CaltechAUTHORS:20100917-135750637
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20020
Deposited By: Ruth Sustaita
Deposited On:17 Sep 2010 21:14
Last Modified:08 Nov 2021 23:56

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