Lie Groups and mechanics: an introduction

Boris Kolev (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Lie groups; geodesic flow; diffeomorphism group of the circle

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Théorie des groupes [math.GR]; Géométrie symplectique [math.SG]; Equations aux dérivées partielles [math.AP]

Boris Kolev. Lie Groups and mechanics: an introduction. Wave motion, Jan 2004, Oberwolfach, Germany. pp.480-498, ⟨10.2991/jnmp.2004.11.4.5⟩. ⟨hal-00001155v2⟩