The inverse problem of the calculus of variations for discrete systems

BARBERO-LIÑÁN, MARÍA; FARRÉ PUIGGALÍ, MARTA; FERRARO, SEBASTIÁN JOSÉ; MARTÍN DE DIEGO, DAVID

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2018 vol. 51 p. 185 - 202

1751-8113

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 for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.