ESAIM: COCV, Vol. 14, N°2, pp. 356-380
DOI: 10.1051/cocv:2007056

Variational calculus on Lie algebroids

Eduardo Martínez

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain; emf@unizar.es

(Received July 14, 2006. Published online October 13, 2007.)

Abstract
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

Mathematics Subject Classification. 49S05, 49K15, 58D15, 70H25, 17B66, 22A22

Key words: Variational calculus, Lagrangian mechanics, Lie algebroids, reduction of dynamical systems, Euler-Poincaré equations, Lagrange-Poincaré equations


© EDP Sciences, SMAI 2008