Implicit Lagrange-Routh equations and Dirac reduction

Eduardo García-Toraño Andrés, Tom Mestdag, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can be described in the context of dynamical systems associated to Dirac structures, in which we fully utilize a symmetry reduction procedure for implicit Hamiltonian systems with symmetry.

    Original languageEnglish
    Pages (from-to)291-304
    Number of pages14
    JournalJournal of Geometry and Physics
    Volume104
    DOIs
    Publication statusPublished - 2016 Jun 1

    Fingerprint

    Lagrange Equation
    Paul Adrien Maurice Dirac
    pontryagin principle
    symmetry
    Pontryagin's Principle
    Dirac Structures
    Symmetry
    regularity
    dynamical systems
    Lagrangian Systems
    Symmetry Reduction
    bundles
    Regularity Conditions
    Reduction Method
    Submanifolds
    Hamiltonian Systems
    momentum
    Bundle
    Momentum
    Dynamical system

    Keywords

    • Dirac structures
    • Hamilton-Pontryagin principle
    • Implicit Lagrange-Routh equations
    • Routh reduction

    ASJC Scopus subject areas

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

    Cite this

    Implicit Lagrange-Routh equations and Dirac reduction. / García-Toraño Andrés, Eduardo; Mestdag, Tom; Yoshimura, Hiroaki.

    In: Journal of Geometry and Physics, Vol. 104, 01.06.2016, p. 291-304.

    Research output: Contribution to journalArticle

    García-Toraño Andrés, Eduardo ; Mestdag, Tom ; Yoshimura, Hiroaki. / Implicit Lagrange-Routh equations and Dirac reduction. In: Journal of Geometry and Physics. 2016 ; Vol. 104. pp. 291-304.
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