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The exact discrete Lagrangian function on a Lie groupoid: theory and applications Marrero, Juan Carlos

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In this talk, I will present some recent results on the geometric construction of the exact discrete Lagrangian function associated with a continuous regular Lagrangian function. This Lagrangian function is defined on the Lie algebroid of a Lie groupoid. In the last part of the talk, I will discuss two applications of the previous construction: i) Analysis of the error between the exact solutions of the Euler-Lagrange equations for the continuous Lagrangian function and the discrete trajectories derived by a variational integrator and ii) A relation with the Hamilton-Jacobi theory for the Hamiltonian function associated with the regular Lagrangian function.

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