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Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids

AutorMarrero, Juan Carlos; Martín de Diego, David; Martínez, Eduardo
Palabras claveDiscrete Mechanics
Lie groupoids
Lie algebroids
Lagrangian Mechanics
Hamiltonian Mechanics
Fecha de publicación27-nov-2006
EditorInstitute of Physics Publishing
CitaciónarXiv:math/0506299v2
Nonlinearity, vol. 19, no. 6 (Jun. 2006), pp. 1313-1348.
ResumenThe 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.
URIhttp://hdl.handle.net/10261/2283
ISSN0951-7715
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