The inverse problem of the calculus of variations for discrete systems

María Barbero-Liñán, Marta Farré Puiggalí, Sebastián Ferraro, David Martín de Diego

Published 2017-08-14Version 1

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators.