On the Existence of a Gyroscope in Spaces with Affine Connections and Metrics

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 (a non-null contravariant vector field) of an observer.

Deviation operator and deviation equations over spaces with affine connections and metrics

“…If a (L n , g)-space could be used as a model of space or of space-time the question arises how signals could propagate in a space-time described by a (L n , g)-space. The answer of this question has been given in [19], [20], and [21]. By that the signals are described by means of null (isotropic) vector fields.…”

“…It has been shown [20], [21] that in a (L n , g)-space longitudinal (standard) and transversal Doppler effects could appear when signals are propagating from an emitter to an observer (detector) moving relatively to each other.…”

“…1. Let a signal with frequency ω be emitted by an emitter [20] at the time τ − dτ and be received by an observer (detector) at the time τ .…”

“…Hubble effect and the shift frequency parameter 1. By the use of the relations [20], [21] l vηc = ∓H c · l ξ ⊥ , l aηc = ∓q ηc · l ξ ⊥ ,…”

“…Section 4 comprises some concluding remarks. Most of the details and derivations omitted in this paper could be found in [20] and in [21].…”