Relative equilibria in systems with configuration space isotropy

Mark Roberts, Tanya Schmah, Cristina Stoica*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    We present a framework for studying Lagrangian and Hamiltonian systems with symmetries, near points with configuration space isotropy. We use twisted parametrisations corresponding to phase space slices based at zero points of (co-)tangent fibres. Given a hyperregular Lagrangian, we find a Legendre transform in the twisted coordinates. For simple mechanical systems, we state necessary and sufficient conditions for the existence of relative equilibria in terms of an augmented-amended potential.

    Original languageEnglish
    Pages (from-to)762-779
    Number of pages18
    JournalJournal of Geometry and Physics
    Volume56
    Issue number5
    DOIs
    Publication statusPublished - May 2006

    Keywords

    • Augmented-amended potential
    • Bundle equations
    • Legendre transform
    • Reconstruction equations
    • Relative equilibria
    • Slice theorem

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