On the existence of a gyroscope in spaces with affine connections and metrics

TL;DR

This paper investigates the conditions necessary for the existence of gyroscopes in spaces characterized by affine connections and metrics, framing them as special Fermi-Walker transports orthogonal to an observer's velocity.

Contribution

It derives specific conditions under which gyroscopes can exist in such geometric spaces, expanding the understanding of transport mechanisms in affine-metric geometries.

Findings

Identifies conditions for gyroscope existence in affine-metric spaces.

Relates gyroscope transport to Fermi-Walker transport types.

Provides mathematical framework for gyroscope behavior in these spaces.

Abstract

Conditions for the existence of a gyroscope in spaces with affine connections and metrics are found. They appear as special types of Fermi-Walker transports for vector fields, lying in a subspace, orthogonal to the velocity vector field of an observer. PACS numbers: 04.20Cv, 04.90.+e, 04.50.+h, 02.40.Ky