Nonlinear Dynamics of Cylindrical Resonator of Wave Solid-State Gyroscope with Electromagnetic Control Sensors

The article considers the nonlinear dynamics of a cylindrical resonator of a wave solid-state gyroscope with electromagnetic control sensors. A mathematical model that describes nonlinear resonator oscillations and electrical processes of the oscillation control circuit in an interconnected form is deduced. The resulting mathematical model represents a nonlinear system of differential equations, which contains singularly perturbed equations, and the equations of electrical processes are singularly perturbed. The nonlinearity caused by the finite ratio of the small deflection to the small gap of the control sensor is taken into account. The methods of constructing approximate solutions are proposed. The fundamental difference between the nonlinear terms of the equations of resonator dynamics using eight and sixteen control sensors is shown. It is shown that by using electromagnetic control sensors it is necessary to take into account a small parameter singularly included in the differential equations of electrical processes. According to the estimation of the angular drift velocity, it is concluded that the gyroscope circuit with eight electromagnetic control sensors is inapplicable due to the obtained value of the uncompensated angular drift velocity. In the case of a gyroscope with sixteen control sensors, a formula for the angular drift velocity which can be compensated is derived and a method for calculating the displacement of the resonant peak of the amplitude-frequency response is proposed.