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 publicationLecture Notes in Control and Information Sciences
    Pages233-247
    Number of pages15
    Volume366 LNCIS
    Publication statusPublished - 2007
    Event3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006 - Nagoya
    Duration: 2006 Jul 192006 Jul 21

    Publication series

    NameLecture Notes in Control and Information Sciences
    Volume366 LNCIS
    ISSN (Print)01708643

    Other

    Other3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006
    CityNagoya
    Period06/7/1906/7/21

    ASJC Scopus subject areas

    • Library and Information Sciences

    Cite this

    Yoshimura, H., & Marsden, J. E. (2007). Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. In Lecture Notes in Control and Information Sciences (Vol. 366 LNCIS, pp. 233-247). (Lecture Notes in Control and Information Sciences; Vol. 366 LNCIS).

    Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. / Yoshimura, Hiroaki; Marsden, Jerrold E.

    Lecture Notes in Control and Information Sciences. Vol. 366 LNCIS 2007. p. 233-247 (Lecture Notes in Control and Information Sciences; Vol. 366 LNCIS).

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

    Yoshimura, H & Marsden, JE 2007, Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. in Lecture Notes in Control and Information Sciences. vol. 366 LNCIS, Lecture Notes in Control and Information Sciences, vol. 366 LNCIS, pp. 233-247, 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006, Nagoya, 06/7/19.
    Yoshimura H, Marsden JE. Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. In Lecture Notes in Control and Information Sciences. Vol. 366 LNCIS. 2007. p. 233-247. (Lecture Notes in Control and Information Sciences).
    Yoshimura, Hiroaki ; Marsden, Jerrold E. / Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. Lecture Notes in Control and Information Sciences. Vol. 366 LNCIS 2007. pp. 233-247 (Lecture Notes in Control and Information Sciences).
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