Simple evaluation of Casimir invariants in finite-dimensional Poisson systems

TL;DR

This paper introduces a straightforward algebraic method for calculating Casimir functions in finite-dimensional Poisson systems, simplifying the traditionally complex process of solving partial differential equations.

Contribution

It presents a novel algebraic approach that significantly reduces the difficulty of finding Casimir invariants in finite-dimensional Poisson systems.

Findings

Algebraic manipulation of the structure matrix simplifies calculations

Method avoids solving PDEs traditionally used for Casimir functions

Procedure is efficient for finite-dimensional Poisson systems

Abstract

In this letter we present a procedure for the calculation of the Casimir functions of finite-dimensional Poisson systems which avoids the burden of solving a set of partial differential equations, as it is usually suggested in the literature. We show how a simple algebraic manipulation of the structure matrix reduces substantially the difficulty of the problem.