On Dirac structures admitting a variational approach

TL;DR

This paper explores the cohomological properties of Dirac structures and Lie algebroids to identify obstructions to formulating Dirac dynamics through variational principles.

Contribution

It introduces a basic cohomology framework for Dirac structures and uses it to characterize when a variational formulation is possible.

Findings

Identifies cohomological obstructions to variational formulations of Dirac dynamics.

Provides a new perspective on the structure of Dirac systems.

Establishes a link between cohomology and variational principles in geometric mechanics.

Abstract

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.