On the exact discrete Lagrangian function for variational integrators: theory and applications

Abstract

In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descriptions as, for instance, Euler-Lagrange equations, Euler-Poincaré equations, Lagrange-Poincaré equations... The construction of an exact discrete Lagrangian is of considerable interest for the analysis of the error between an exact trajectory and the discrete trajectory derived by a variational integrator.

40 pages

Cited by in corpus (7)

• Variational order for forced Lagrangian systems
• Retraction maps: a seed of geometric integrators
• On the Geometry of the Hamilton-Jacobi Equation and Generating Functions
• Error analysis of forced discrete mechanical systems
• The inverse problem of the calculus of variations for discrete systems
• Lie-Poisson integrators
• A Discrete Variational Derivation of Accelerated Methods in Optimization