On tensor invariants for integrable cases of Euler, Lagrange and Kovalevskaya rigid body motion

TL;DR

This paper investigates global tensor invariants in classical rigid body motions, specifically Euler, Lagrange, and Kovalevskaya cases, using algebraic methods and computer algebra systems to understand their role in dynamics.

Contribution

It introduces a method to find tensor invariants by solving algebraic equations derived from invariance conditions, advancing the understanding of invariant structures in rigid body dynamics.

Findings

Identified new tensor invariants for specific rigid body cases.

Demonstrated the use of computer algebra systems in solving invariance equations.

Linked invariants to the study of geometric structures in dynamics.

Abstract

We discuss global tensor invariants of a rigid body motion in the cases of Euler, Lagrange and Kovalevskaya. These invariants are obtained by substituting tensor fields with cubic on variable components into the invariance equation and solving the resulting algebraic equations using computer algebra systems. According to the Poincar\'{e}-Cartan theory of invariants, the existence of invariant geometric structures raises the question of using them to study the dynamics.