no. 2
Variational calculus on Lie algebroids
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 356-380.

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.

DOI : 10.1051/cocv:2007056
Classification : 49S05, 49K15, 58D15, 70H25, 17B66, 22A22
Mots clés : variational calculus, lagrangian mechanics, Lie algebroids, reduction of dynamical systems, Euler-Poincaré equations, Lagrange-Poincaré equations 
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     title = {Variational calculus on {Lie} algebroids},
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     pages = {356--380},
     publisher = {EDP-Sciences},
     volume = {14},
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Martínez, Eduardo. Variational calculus on Lie algebroids. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 356-380. doi : 10.1051/cocv:2007056. http://www.numdam.org/articles/10.1051/cocv:2007056/

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