Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrohrads'kyj mechanics

TL;DR

This paper investigates the symmetries of vector exterior differential systems within variational problems, applying the framework to third-order equations of motion for a semi-classical spinning particle, advancing understanding of their geometric structure.

Contribution

It introduces a novel approach to analyze symmetries of variational problems using vector bundle valued exterior differential systems, specifically applied to higher-order particle dynamics.

Findings

Identifies symmetry properties of third-order variational equations.

Provides a geometric framework for the inverse problem in Ostrohrads'kyj mechanics.

Enhances understanding of symmetries in semi-classical spinning particle models.

Abstract

Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variational equations of motion of the semi-classical spinning particle.