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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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)
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creator Barbero-Liñán, María
Marta Farré Puiggalí
Ferraro, Sebastián
Martín de Diego, David
description 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.
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subjects Calculus of variations
Computer simulation
Discrete systems
Integrators
Inverse problems
Manifolds (mathematics)
Mathematical analysis
Mechanics (physics)
title The inverse problem of the calculus of variations for discrete systems
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