Session A5 - Geometric Integration and Computational Mechanics
July 10, 18:00 ~ 18:30
The inverse problem for discrete systems
Marta Farré Puiggalí
ICMAT, Spain - email@example.com
The classical inverse problem of the calculus of variations consists in determining whether or not a given system of explicit second order differential equations is equivalent to a system of Euler-Lagrange equations for some regular Lagrangian. We will develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics, using suitable Lagrangian and isotropic submanifolds. We will 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 of geometric integrators.
Joint work with María Barbero Liñán (Universidad Politécnica de Madrid, Spain), Sebastián Ferraro (Universidad Nacional del Sur, Argentina) and David Martín de Diego (ICMAT, Spain).