On gyroscopic precession

TL;DR

This paper develops a theoretical framework to describe gyroscopic precession relative to arbitrary reference congruences, clarifying the role of vorticity and supporting experimental analysis.

Contribution

It derives the evolution equation for a gyroscope's angular momentum relative to any time-like congruence, extending understanding beyond the standard vorticity interpretation.

Findings

Derived the evolution equation for gyroscopic angular momentum.

Identified conditions linking vorticity to gyroscopic precession.

Provided theoretical basis for experimental analysis of gyroscopic precession.

Abstract

The vorticity of a congruence is often considered to be the rate of rotation for the precession of a gyroscope moving along a world-line belonging to that congruence. Our aim here was to determine the evolution equation for the angular momentum of a gyrosocope with respect to an arbitrary time-like congruence: i.e, a reference congruence not containing the curve described by the gyroscope. In particular, we show the specific conditions needed to support the introductory statement about the vorticity. We thus establish a well-founded theoretical description for the analysis of the precession of gyroscopes, providing suitable conclusions for possible experiments.