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## Archive of Issues

Russia Izhevsk
Year
2019
Volume
29
Issue
1
Pages
84-91
 Section Mechanics Title Model of the hemispherical resonator gyroscope construction damping Author(-s) Trutnev G.A.a Affiliations Udmurt State Universitya Abstract This article is concerned with the hemispherical resonator gyroscope, a device for measurement of the projection of the angular speed to a device axis. The basic element of the device is a resonator in which the effect of inertness of standing waves is implemented. Various defects of materials and manufacturing techniques lead to an interaction between the main working fluctuations and collateral deformations in the location of fastening, resulting in construction damping and hence in the drift of a standing wave. Problems of constructional damping in the hemispherical resonator gyroscope and emergence of drift of a wave by means of modeling in the form of a mechanical system are investigated. A mathematical model is derived using Lagrange's approach. A mechanical system is described in Cartesian coordinates in general form for the $N+1$ mass. In the mechanical system, the central weight models a fixing leg of the resonator. A more convenient coordinate system for the description of the mechanical system is chosen. Calculations for obtaining a mathematical model in the form of a system of differential equations are carried out. The resulting mathematical model is analyzed. Avenues of further research on a construction damping and drift are described. Keywords hemispherical resonator gyroscope, resonator, constructional damping, unbalanced mass of the resonator, drift of a wave, resonator model, mechanical systems, Lagrange's equation UDC 531.383, 534.08, 517.934 MSC 70H03 DOI 10.20537/vm190108 Received 14 January 2019 Language Russian Citation Trutnev G.A. Model of the hemispherical resonator gyroscope construction damping, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. 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