dorsal/arxiv
View Schema"Falling cat" connections and the momentum map
| Authors | Marian Fecko |
|---|---|
| Categories | |
| ArXiv ID | physics/9702010 |
| URL | https://arxiv.org/abs/physics/9702010 |
| DOI | 10.1063/1.531183 |
| Journal | J.Math.Phys. 36 (12) 6709-6719 (1995) |
Abstract
We consider a standard symplectic dynamics on TM generated by a natural Lagrangian L. The Lagrangian is assumed to be invariant with respect to the action TR_g of a Lie group G lifted from the free and proper action R_g of G on M. It is shown that under these conditions a connection on principal bundle pi: M \rightarrow M/G can be constructed based on the momentum map corresponding to the action TR_g. The horizontal motion is shown to be in physical terms the one with all the momenta corresponding to the symmetry vanishing. A simple explicit formula for the connection form is given. For the special case of the standard action of G = SO(3) on M = R^3 x ... x R^3 corresponding to a rigid rotation of a N-particle system the formula obtained earlier by Guichardet and Shapere/Wilczek is reproduced.
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"abstract": "We consider a standard symplectic dynamics on TM generated by a natural\nLagrangian L. The Lagrangian is assumed to be invariant with respect to the\naction TR_g of a Lie group G lifted from the free and proper action R_g of G on\nM. It is shown that under these conditions a connection on principal bundle pi:\nM \\rightarrow M/G can be constructed based on the momentum map corresponding to\nthe action TR_g. The horizontal motion is shown to be in physical terms the one\nwith all the momenta corresponding to the symmetry vanishing. A simple explicit\nformula for the connection form is given. For the special case of the standard\naction of G = SO(3) on M = R^3 x ... x R^3 corresponding to a rigid rotation of\na N-particle system the formula obtained earlier by Guichardet and\nShapere/Wilczek is reproduced.",
"arxiv_id": "physics/9702010",
"authors": [
"Marian Fecko"
],
"categories": [
"math-ph",
"dg-ga",
"math.DG",
"math.MP"
],
"doi": "10.1063/1.531183",
"journal_ref": "J.Math.Phys. 36 (12) 6709-6719 (1995)",
"title": "\"Falling cat\" connections and the momentum map",
"url": "https://arxiv.org/abs/physics/9702010"
},
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