Variational calculus on Lie algebroids

Eduardo Martínez

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 2, page 356-380
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Martínez, Eduardo. "Variational calculus on Lie algebroids." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 356-380. <http://eudml.org/doc/250369>.

@article{Martínez2008,
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. },
author = {Martínez, Eduardo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Variational calculus; Lagrangian mechanics; Lie algebroids; reduction of dynamical systems; Euler-Poincaré equations; Lagrange-Poincaré equations; variational calculus},
language = {eng},
month = {3},
number = {2},
pages = {356-380},
publisher = {EDP Sciences},
title = {Variational calculus on Lie algebroids},
url = {http://eudml.org/doc/250369},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Martínez, Eduardo
TI - Variational calculus on Lie algebroids
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/3//
PB - EDP Sciences
VL - 14
IS - 2
SP - 356
EP - 380
AB - 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.
LA - eng
KW - Variational calculus; Lagrangian mechanics; Lie algebroids; reduction of dynamical systems; Euler-Poincaré equations; Lagrange-Poincaré equations; variational calculus
UR - http://eudml.org/doc/250369
ER -

References

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