On Dirac Structures Admitting A Variational Approach

Oscar Cosserat (1) , Alexei Kotov (2) , Camille Laurent-Gengoux (3) , Leonid Ryvkin (4, 5, 6) , Vladimir Salnikov (1)

1 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356
2 University of Hradec Králové
3 IECL - Institut Élie Cartan de Lorraine
4 Georg-August-University = Georg-August-Universität Göttingen
5 ICJ - Institut Camille Jordan
6 PSPM - Probabilités, statistique, physique mathématique

We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formulation of Dirac dynamics.

Domaines: Géométrie différentielle [math.DG]; Physique mathématique [math-ph]

Oscar Cosserat, Alexei Kotov, Camille Laurent-Gengoux, Leonid Ryvkin, Vladimir Salnikov. On Dirac Structures Admitting A Variational Approach. Mathematics and Mechanics of Complex Systems, 2023, 11 (1), pp.1-18. ⟨10.2140/memocs.2023.11.1⟩. ⟨hal-03445074v2⟩