Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems

Hiroaki Yoshimura, Jerrold E. Marsden

    Research output: Contribution to journalArticle

    73 Citations (Scopus)

    Abstract

    This paper develops the notion of implicit Lagrangian systems and presents some of their basic properties in the context of Dirac structures. This setting includes degenerate Lagrangian systems and systems with both holonomic and nonholonomic constraints, as well as networks of Lagrangian mechanical systems. The definition of implicit Lagrangian systems with a configuration space Q makes use of Dirac structures on T* Q that are induced from a constraint distribution on Q as well as natural symplectomorphisms between the spaces T* T Q, T T* Q, and T* T* Q. Two illustrative examples are presented; the first is a nonholonomic system, namely a vertical disk rolling on a plane, and the second is an L-C circuit, a degenerate Lagrangian system with holonomic constraints.

    Original languageEnglish
    Pages (from-to)133-156
    Number of pages24
    JournalJournal of Geometry and Physics
    Volume57
    Issue number1
    DOIs
    Publication statusPublished - 2006 Dec 31

    Fingerprint

    Lagrangian Mechanics
    Dirac Structures
    Lagrangian Systems
    Rolling Disk
    Nonholonomic Constraints
    Nonholonomic Systems
    Configuration Space
    Mechanical Systems
    Vertical
    configurations

    Keywords

    • Dirac structures
    • Implicit Lagrangian systems
    • Nonholonomic systems

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Geometry and Topology

    Cite this

    Dirac structures in Lagrangian mechanics Part I : Implicit Lagrangian systems. / Yoshimura, Hiroaki; Marsden, Jerrold E.

    In: Journal of Geometry and Physics, Vol. 57, No. 1, 31.12.2006, p. 133-156.

    Research output: Contribution to journalArticle

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