Dynamics of a micromechanical dual-mass gyroscope of RL-type in a free oscillation mode

This paper presents the analysis of a mechanical and theoretical model of a micromechanical RL-type gyroscope (MMG). The behavior of the resonator in a free oscillation mode is studied by solving the problem in a linear formulation. The main part of the paper is devoted to the mathematical model development for a dual-mass MMG with a disk-shaped resonator, which is fixed on the elastic leg on a movable base. The important condition of the problem implies the arbitrary angular velocity of the base Omega. The derived equations are analyzed in terms of orbital coordinates (r, k, theta, chi). The equations determining the precession angle (theta) of the considered gyroscope are obtained. A brief analysis of the proposed dependences and the corresponding conclusions about the behavior of the system under free oscillations are presented.