The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a thirdsection we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and theCamassa-Holm equation.
Publié le : 2004-01-05
Classification:
Lie groups,
geodesic flow,
diffeomorphism group of the circle,
58B25; 22E65; 35Q35,
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],
[MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00001155,
author = {Kolev, Boris},
title = {Lie Groups and mechanics: an introduction},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00001155}
}
Kolev, Boris. Lie Groups and mechanics: an introduction. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001155/