Effects of imperfections on solid-wave gyroscope dynamics

Solid-wave gyroscopes are symmetric resonators that sense rotation by measuring how Coriolis forces perturb a degenerate mode pair. The idealized dynamics of these devices are described by ODE models of two identical oscillators coupled by a perturbation due to rotation. In miniaturized solid-wave gyroscopes, geometric distortions due to imperfect fabrication also perturb the dynamics, and this limits sensing accuracy. In this work, we describe how geometric imperfections affect the dynamics of solid-wave gyroscopes. We also use selection rules both to find qualitative information about what types of geometry perturbations most affect sensor performance and to accelerate computations.