Tangent Euler Top in General Relativity

TL;DR

This paper introduces the tangent Euler top in General Relativity, deriving its equations of motion and showing their relation to the Mathisson-Papapetrou equations through approximation methods.

Contribution

It defines the tangent Euler top within the framework of General Relativity and connects its dynamics to established equations of motion.

Findings

Derivation of the tangent Euler top via a constrained Lagrangian.

Lowest-order approximation yields Mathisson-Papapetrou equations.

Provides a new geometric perspective on spinning bodies in GR.

Abstract

We define the tangent Euler top in General Relativity through a constrained Lagrangian on the orthonormal frame bundle. The corresponding motions are studied to various degrees of approximation, the lowest of which is shown to yield the Mathisson-Papapetrou equations.