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 |
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Pages (from-to) | 762-779 |
Number of pages | 18 |
Journal | Journal of Geometry and Physics |
Volume | 56 |
Issue number | 5 |
DOIs | |
Publication status | Published - May 2006 |
Keywords
- Augmented-amended potential
- Bundle equations
- Legendre transform
- Reconstruction equations
- Relative equilibria
- Slice theorem