Morse families and Dirac systems
Mathematical Physics
2021-03-16 v1 Dynamical Systems
math.MP
Abstract
Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples in the paper show. This approach generalizes the previous results on Dirac structures associated with Lagrangian submanifolds. An integrability algorithm in the sense of Mendela, Marmo and Tulczyjew is described for the generalized Dirac dynamical systems under study to determine the set where the implicit differential equations have solutions.
Cite
@article{arxiv.1804.04949,
title = {Morse families and Dirac systems},
author = {M. Barbero-Liñán and H. Cendra and E. García-Toraño Andrés and D. Martín de Diego},
journal= {arXiv preprint arXiv:1804.04949},
year = {2021}
}
Comments
this article supersedes the first part of arXiv:1702.08596