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A Survey of Lagrangian Mechanics and Control on Lie algebroids and groupoids

AuthorsCortés, Jorge; León, Manuel de; Marrero, Juan Carlos; Martín de Diego, David; Martínez, Eduardo
KeywordsLie algebroids
Lie groupoids
Lagrangian Mechanics
Hamiltonian Mechanics
Nonholonomic Lagrangian systems
Mechanical control systems
Discrete mechanics
Classical field theory
Issue Date3-Nov-2005
PublisherWorld Scientific Publishing
International Journal of Geometric Methods in Modern Physics, 3(3): 509-558 (2006)
AbstractIn 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.
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