Geodesic
Dynamics of a micromechanical dual-mass gyroscope of $RL$-type in a free oscillation mode
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 82 (2023), pp. 55-65

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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.
Keywords: micromechanical gyroscope, free oscillations, precession angle, tuning fork. 
@article{VTGU_2023_82_a4,
     author = {E. A. Antonov and O. V. Gribova},
     title = {Dynamics of a micromechanical dual-mass gyroscope of $RL$-type in a free oscillation mode},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {55--65},
     publisher = {mathdoc},
     number = {82},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_82_a4/}
}
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E. A. Antonov; O. V. Gribova. Dynamics of a micromechanical dual-mass gyroscope of $RL$-type in a free oscillation mode. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 82 (2023), pp. 55-65. http://geodesic.mathdoc.fr/item/VTGU_2023_82_a4/