Recursive properties of Dirac and Metriplectic Dirac brackets with Applications

TL;DR

This paper demonstrates that Dirac brackets for constrained systems can be derived recursively and explores their application in physical models, emphasizing computational implementation and matrix inversion techniques.

Contribution

It introduces a recursive method for deriving Dirac brackets and analyzes their practical application and computational aspects in physical models.

Findings

Recursive derivation of Dirac brackets for constrained systems.

Feasibility of implementing Dirac brackets in Computer Algebra Systems.

Analytical techniques for inverting triangular matrices.

Abstract

In this article, we prove that Dirac brackets for Hamiltonian and non-Hamiltonian constrained systems can be derived recursively. We then study the applicability of that formulation in analysis of some interesting physical models. Particular attention is paid to the feasibility of implementation code for Dirac brackets in Computer Algebra System and analytical techniques for inversion of triangular matrices.