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Variational calculus on Lie algebroids

Published online by Cambridge University Press:  20 March 2008

Eduardo Martínez
Eduardo Martínez*
Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain; emf@unizar.es
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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.

Keywords

Variational calculusLagrangian mechanicsLie algebroidsreduction of dynamical systemsEuler-Poincaré equationsLagrange-Poincaré equations

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008, pp. 356 - 380
Copyright
© EDP Sciences, SMAI, 2008

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