Morse families and Dirac systems

Authors

María Barbero Liñán, Hernán Cendra, Eduardo García Toraño, David Martín de Diego

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.

Citation

• Journal: Journal of Geometric Mechanics
• Year: 2019
• Volume: 11
• Issue: 4
• Pages: 487–510
• Publisher: American Institute of Mathematical Sciences (AIMS)
• DOI: 10.3934/jgm.2019024

BibTeX

@article{Barbero_Li_n_2019,
  title={{Morse families and Dirac systems}},
  volume={11},
  ISSN={1941-4897},
  DOI={10.3934/jgm.2019024},
  number={4},
  journal={Journal of Geometric Mechanics},
  publisher={American Institute of Mathematical Sciences (AIMS)},
  author={Barbero Liñán, María and Cendra, Hernán and García Toraño, Eduardo and Martín de Diego, David},
  year={2019},
  pages={487--510}
}

Download the bib file

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