The inverse problem of the calculus of variations for discrete systems

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...

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Bibliographic Details
Published in:arXiv.org 2017-08
Main Authors: Barbero-Liñán, María, Marta Farré Puiggalí, Ferraro, Sebastián, Martín de Diego, David
Format: Article
Language:English
Subjects:
Calculus of variations
Computer simulation
Discrete systems
Integrators
Inverse problems
Manifolds (mathematics)
Mathematical analysis
Mechanics (physics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1708.04123