Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 050, 17 pages      math-ph/0703062      https://doi.org/10.3842/SIGMA.2007.050
Contribution to the Proceedings of the Coimbra Workshop on Geometric Aspects of Integrable Systems

Lie Algebroids in Classical Mechanics and Optimal Control

Eduardo Martínez
Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received November 07, 2006, in final form March 07, 2007; Published online March 20, 2007

Abstract
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.

Key words: Lagrangian mechanics; Lie algebroids; variational calculus; reduction of dynamical systems; optimal control systems.

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