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Symmetry reduction of discrete Lagrangian mechanics on Lie groups

Abstract:

For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group $G$ of the canonical discrete Lagrange 2-form $\omega_\mathbb{L}$ on $G \times G$. Its symplectic leaves then become dyna...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Journal of Geometry and Physics More from this journal
Volume:
36
Issue:
1-2
Pages:
140-151
Publication date:
2000-04-04
DOI:
ISSN:
0393-0440
Keywords:
Pubs id:
pubs:404792
UUID:
uuid:f8d5106e-c626-4c89-9733-1dd53b19142e
Local pid:
pubs:404792
Source identifiers:
404792
Deposit date:
2013-11-16

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