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lagrange-poincaré equations

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Variational calculus on Lie algebroids
Eduardo Martínez
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 2 / April 2008

Published online by Cambridge University Press:

20 March 2008, pp. 356-380

Print publication:

April 2008
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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.