"Falling cat" connections and the momentum map
Fecko, Marian
arXiv, 9702010 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1997-02-12
Classification:  Mathematical Physics,  Mathematics - Differential Geometry 
@article{9702010,
     author = {Fecko, Marian},
     title = {"Falling cat" connections and the momentum map},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9702010}
}

Fecko, Marian. "Falling cat" connections and the momentum map. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9702010/