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

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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
Keywords: variational calculus, lagrangian mechanics, Lie algebroids, reduction of dynamical systems, Euler-Poincaré equations, Lagrange-Poincaré equations 
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     author = {Mart{\'\i}nez, Eduardo},
     title = {Variational calculus on {Lie} algebroids},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {356--380},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {2},
     year = {2008},
     doi = {10.1051/cocv:2007056},
     mrnumber = {2394515},
     zbl = {1135.49027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007056/}
}
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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

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