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.

摘要-考虑到振动激发的静电系统的影响，已经为波动固态陀螺仪的单晶谐振器的运动构建了一个新的数学模型，该模型以在运动基座上旋转的弹性薄壳形式存在， 。对于谐振器的弹性变形的势能得出的表达式考虑了立方晶型的低各向异性，这取决于谐振器相对于晶体轴的取向。离散模型用于描述控制传感器静电场的能量。使用Lagrange-Maxwell形式主义，获得了非线性微分方程，这些方程以单模逼近描述了在移动基座上旋转的弹性壳的振动。考虑了谐振器的强迫和自由振荡。结果表明，可以通过控制传感器的静电力来补偿由谐振器材料的弹性各向异性引起的系统误差。建议使用控制信号来补偿这些误差。