The inverse problem of the calculus of variations for discrete systems
arXiv:1708.04123 · doi:10.1088/1751-8121/aab546
Abstract
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.
arXiv comment30 pages
References in corpus (6)
- Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
- Momentum and energy preserving integrators for nonholonomic dynamics
- Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations
- Modified Equations for Variational Integrators
- On the exact discrete Lagrangian function for variational integrators: theory and applications
- Isotropic submanifolds and the inverse problem for mechanical constrained systems