We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold $M$; the set of units is the zero section identified with the manifold $M$. We study the Legendre transformation on Lie algebroids.
@article{107570,
author = {Paulette Libermann},
title = {Lie algebroids and mechanics},
journal = {Archivum Mathematicum},
volume = {032},
year = {1996},
pages = {147-162},
zbl = {0912.70009},
mrnumber = {1421852},
language = {en},
url = {http://dml.mathdoc.fr/item/107570}
}
Libermann, Paulette. Lie algebroids and mechanics. Archivum Mathematicum, Tome 032 (1996) pp. 147-162. http://gdmltest.u-ga.fr/item/107570/
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