Lie Algebroids in Classical Mechanics and Optimal Control

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• ISSN: 1815-0659
• Main Author: Martínez, E.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147813
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Lie Algebroids in Classical Mechanics and Optimal Control / E. Martínez // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ.

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.