Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems

Hiroaki Yoshimura, Jerrold E. Marsden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationLagrangian and Hamiltonian Methods for Nonlinear Control 2006 - Proceedings from the 3rd IFAC Workshop
PublisherSpringer Verlag
Pages233-247
Number of pages15
ISBN (Print)3540738894, 9783540738893
DOIs
Publication statusPublished - 2007 Jan 1
Event3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006 - Nagoya, Japan
Duration: 2006 Jul 192006 Jul 21

Publication series

NameLecture Notes in Control and Information Sciences
Volume366 LNCIS
ISSN (Print)0170-8643

Conference

Conference3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006
CountryJapan
CityNagoya
Period06/7/1906/7/21

ASJC Scopus subject areas

  • Library and Information Sciences

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    Yoshimura, H., & Marsden, J. 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 (pp. 233-247). (Lecture Notes in Control and Information Sciences; Vol. 366 LNCIS). Springer Verlag. https://doi.org/10.1007/978-3-540-73890-9_18