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IssuesArchive of Issues2022-8pp.1830-1847

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B.I. Konosevich and Yu.B. Konosevich, "Gyrostat with an Electric Motor: a Mathematical Model and Stationary Motions," Mech. Solids. 57 (8), 1830-1847 (2022)
Year 2022 Volume 57 Number 8 Pages 1830-1847
DOI 10.3103/S0025654422080180
Title Gyrostat with an Electric Motor: a Mathematical Model and Stationary Motions
Author(s) B.I. Konosevich (Institute of Applied Mathematics and Mechanics, Donetsk, Russia, konos.donetsk@yandex.ru)
Yu.B. Konosevich (Institute of Applied Mathematics and Mechanics, Donetsk, Russia)
Abstract A mathematical model of a single-rotor gyrostat with a fixed point in the gravity field is proposed. The gyrostat is equipped with an electric motor that maintains spinning of a rotor in the presence of the dissipative moment on its axis. It is assumed that spherical hinge that implements the fixed point is free of friction. Currentless models of the asynchronous and synchronous electric motors and a multiple-current model of the synchronous electric motor are considered. For the gyrostat with the electric motor, two forms of equations of motion have been derived, which correspond to two definitions of the inertia tensor. Conditions for the existence of stationary solutions of these equations have been analyzed. These solutions describe stationary motions of the gyrostat: permanent rotation around a vertical axis and the state of rest of the carrier. The conditions found are compared with the similar conditions for two known models of the gyrostat: with a rotor spinning at a constant angular velocity and by inertia without friction. The directions of the semiaxes of the steady rotation of the gyrostat with the electric motor are shown in the general case to form in the carrier a cone that coincides with the cone of the semiaxes of the steady rotation of the gyrostat with a steadily spinning rotor.
Keywords gyrostat, inertia tensor, asynchronous and synchronous electric motor, stationary motion, cone of semiaxes of steady rotations
Received 27 January 2022Revised 08 July 2022Accepted 15 July 2022
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