Lie Algebroids in Classical Mechanics and Optimal Control

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.

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (3)

• Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
• Classical Field theory on Lie algebroids: multisymplectic formalism
• Non-holonomic Lagrangian systems on Lie algebroids

Cited by in corpus (8)

• Prototypes of higher algebroids with applications to variational calculus
• Optimal Control Theory on almost-Lie Algebroids
• Remarks on generalized Lie algebroids and related concepts
• Lagrangian Mechanics and Reduction on Fibered Manifolds
• On almost complex Lie algebroids
• Lie algebroids generated by cohomology operators
• Global controllability tests for geometric hybrid control systems
• Quantum Systems as Lie Algebroids