On application of involutivity analysis of differential equations to constrained dynamical systems

TL;DR

This paper discusses computer methods for involutivity analysis of differential equations and applies them to study degenerate Lagrangian systems, exemplified by light-cone SU(2) Yang-Mills mechanics, implemented in Maple.

Contribution

It introduces a computational approach to involutivity analysis and demonstrates its application to a specific constrained dynamical system.

Findings

Successful implementation of algorithms in Maple

Analysis of degenerate Lagrangian systems

Application to light-cone SU(2) Yang-Mills mechanics

Abstract

A brief sketch of computer methods of involutivity analysis of differential equations is presented in context of its application to study degenerate Lagrangian systems. We exemplify the approach by a detailed consideration of a finite-dimensional model, the so-called light-cone SU(2) Yang-Mills mechanics. All algorithms are realized in computer algebra system Maple.