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.