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• W2019151447 abstract "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-Poincar'e and discrete Lagrange-Poincar'e equations. Our results can be important for the construction of geometric integrators for continuous Lagrangian systems." @default.
• W2019151447 created "2016-06-24" @default.
• W2019151447 creator A5036992611 @default.
• W2019151447 creator A5061941032 @default.
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• W2019151447 date "2006-05-15" @default.
• W2019151447 modified "2023-10-16" @default.
• W2019151447 title "Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids" @default.
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• W2019151447 doi "https://doi.org/10.1088/0951-7715/19/6/006" @default.
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