 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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 2022 | Revised |
08 July 2022 | Accepted |
15 July 2022 |
| Link to Fulltext |
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