Discrete Mechanical Systems in a Dirac Setting: a Proposal

TL;DR

This paper introduces a novel discrete Dirac mechanics framework using Dirac structures, unifying Lagrangian and Hamiltonian systems and accommodating constraints in a discrete setting.

Contribution

It proposes a new discrete Dirac system formulation that generalizes existing mechanics and incorporates constraints within a Dirac structure framework.

Findings

Discrete Dirac systems can recover classical Lagrangian and Hamiltonian systems.

The approach allows for both kinematic and variational constraints.

A new theoretical foundation for discrete mechanics using Dirac structures is established.

Abstract

In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is possible to recover discrete Lagrangian and Hamiltonian systems as particular cases. We also note that this approach allows for kinematic as well as variational constraints.