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Título : Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
Autor : Marrero, Juan Carlos; Martín de Diego, David; Martínez, Eduardo
Palabras clave : Discrete Mechanics
Lie groupoids
Lie algebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Fecha de publicación : 27-nov-2006
Editor: Institute of Physics Publishing
Citación : arXiv:math/0506299v2
Nonlinearity, vol. 19, no. 6 (Jun. 2006), pp. 1313-1348.
Resumen: The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Legendre transformations we define the Hamiltonian evolution operator which is a symplectic map with respect to the canonical symplectic 2-section on the prolongation of the dual of the Lie algebroid of the given groupoid. The equations we get include as particular cases the classical discrete Euler-Lagrange equations, the discrete Euler-Poincaré and discrete Lagrange-Poincaré equations. Our results can be important for the construction of geometric integrators for continuous Lagrangian systems.
URI : http://hdl.handle.net/10261/2283
ISSN: 0951-7715
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