Inertial rotation sensing in three dimensions using coupled electromagnetic ring-gyroscopes

Abstract

A model gyroscope consisting of three coupled, spatially orthogonal electromagnetic ring-resonators is analysed. It is shown that, through an appropriate choice of inter-ring coupling components, the gyroscope can support a three-dimensional circulating or `gyrating` wave which, when subjected to an arbitrarily changing inertial rotation rate, can be described by an evolving wave amplitude state vector or `gyror`. When the effective resonant mode order takes the value N= 1/2 , the state vector transforms as a spinor and the gyrating wave becomes an inertially stable spinning wave. Despite its low sensitivity, this spin-gyroscope device is of interest since the measurable components of its state spinor are directly related to the parameters (angle-axis variables, quaternion components or Cayley-Klein parameters) which specify the orientation of the gyroscope relative to a fixed inertial frame.