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On Dirac structures admitting a variational approach

Oscar Cosserat, Alexei Kotov, Camille Laurent-Gengoux, Leonid Ryvkin and Vladimir Salnikov

Vol. 11 (2023), No. 1, 1–18
DOI: 10.2140/memocs.2023.11.1
Abstract

We discuss the notion of horizontal cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to describe the condition allowing a variational formulation of Dirac dynamics.

Keywords
Dirac structures, variational approach, theoretical mechanics, constraints
Mathematical Subject Classification
Primary: 37J06, 70H30
Secondary: 65P10
Milestones
Received: 10 May 2022
Revised: 18 October 2022
Accepted: 15 December 2022
Published: 23 October 2023

Communicated by Francesco dell'Isola
Authors
Oscar Cosserat
LaSIE – CNRS
University of La Rochelle
17042 La Rochelle Cedex 1
France
Alexei Kotov
Faculty of Science
University of Hradec Králové
50003 Hradec Králové
Czech Republic
Camille Laurent-Gengoux
Institut Élie Cartan de Lorraine (UMR 7502)
Université de Lorraine
57070 Metz
France
Leonid Ryvkin
Georg-August-Universität Göttingen
37073 Göttingen
Germany
Institut Camille Jordan
Université Claude Bernard Lyon 1
69622 Villeurbanne
France
Vladimir Salnikov
LaSIE – CNRS / La Rochelle University
17042 La Rochelle
France