Relative equilibria in systems with configuration space isotropy

Mark Roberts; Tanya Schmah; Cristina Stoica

doi:10.1016/j.geomphys.2005.04.017

Relative equilibria in systems with configuration space isotropy

Mark Roberts, Tanya Schmah, Cristina Stoica^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	762-779
Number of pages	18
Journal	Journal of Geometry and Physics
Volume	56
Issue number	5
DOIs	https://doi.org/10.1016/j.geomphys.2005.04.017
Publication status	Published - May 2006

Keywords

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

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10.1016/j.geomphys.2005.04.017

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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.",

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AU - Schmah, Tanya

AU - Stoica, Cristina

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N2 - 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.

AB - 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.

KW - Augmented-amended potential

KW - Bundle equations

KW - Legendre transform

KW - Reconstruction equations

KW - Relative equilibria

KW - Slice theorem

UR - https://www.scopus.com/pages/publications/27744442358

U2 - 10.1016/j.geomphys.2005.04.017

DO - 10.1016/j.geomphys.2005.04.017

M3 - Article

AN - SCOPUS:27744442358

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VL - 56

SP - 762

EP - 779

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 5

ER -

Relative equilibria in systems with configuration space isotropy

Abstract

Keywords

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