This article presents an analytical study of the dynamics of a micromechanical integrating gyroscope with a disk resonator. A discrete dynamic model of the resonator is obtained, taking into account the axial anisotropy of its mass and stiffness properties, as well as the action of the electrical control system of oscillations. An analysis of the spectral problem of disk vibrations in the plane is carried out. The nonlinear dynamics of the resonator in the regimes of free and parametrically excited vibrations are investigated. In the mode of parametric oscillations, qualitative dependencies of the gyroscopic drift on the operating voltage, angular velocity and parameters of defects are obtained.