A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS-Reference-Cited by-同舟云学术

A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS

Published:2006-05 Issue:03 Volume:03 Page:509-558
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

CORTÉS JORGE¹,DE LEÓN MANUEL²,MARRERO JUAN C.³,DE DIEGO D. MARTÍN⁴,MARTÍNEZ EDUARDO⁵

Affiliation:

1. Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, California 95064, USA

2. Instituto de Matemáticas y Física Fundamental, Consejo, Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain

3. Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain

4. Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones, Científicas, Serrano 123, 28006 Madrid, Spain

5. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Abstract

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887806001211

Reference43 articles.

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4. On the multisymplectic formalism for first order field theories

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