Abstract
Abstract—A new mathematical model has been constructed for the motion of a single-crystal resonator of a wave solid-state gyroscope in the form of a thin elastic shell rotating on a moving base, taking into account the influence of an electrostatic system of oscillations excitation. The expression derived for the potential energy of elastic deformation of the resonator takes into account low anisotropy of the cubic crystal type depending on the resonator orientation relative to the crystallographic axes. A discrete model is used to describe the energy of the electrostatic field of control sensors. Using the Lagrange−Maxwell formalism, nonlinear differential equations are obtained that describe, in the single-mode approximation, the oscillations of the elastic shell rotating on a moving base. The forced and free oscillations of the resonator are considered. It is shown that a systematic error caused by anisotropy of the elastic properties of the resonator material can be compensated by the effect of electrostatic forces of the control sensors. Control signals are proposed to compensate these errors.
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