The purpose of this work is to determine differences in the nonlinearities of mathematical models of dynamics and nonlinear effects of dynamics for the cylindrical resonator of wave solid–state gyroscope using a different number of electrostatic control sensors.

Methods. In this article resonator oscillations nonlinearity caused by finite ratio of the small deflection of the resonator to the small gap of the electrostatic sensor is considered. To construct approximate mathematical models Tikhonov’s theorem on the passage to the limit is used and
a small parameter singularly included in the system of differential equations is also taken into account. The equations of resonator dynamics are averaged by using the Krylov–Bogolyubov method.

Results. The difference between the nonlinear terms in the equations of resonator dynamics with eight and sixteen control sensors is determined. It is found that nonlinear effects are more pronounced in the case of the gyroscope with sixteen control sensors. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are greater than in the case of eight control sensors. It is shown that in the case of eight control sensors, the angular drift velocity has a variable value and also contains a small uncompensated component.

Conclusion. Mathematical models of the dynamics for the cylindrical resonator of wave solid-state gyroscope taking into account the nonlinearities caused by the excitation of oscillations by eight and sixteen electrostatic control sensors are deduced. The difference between the nonlinear effects of the resonator dynamics for wave solid-state gyroscope with different number of control sensors is shown. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are obtained. Conclusions about the applicability of gyroscope with eight control sensors are discussed.