 | | 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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| G.V. Gorr and T.V. Belokon, "On Solutions of the Equations of Motion of a Gyrostat with a Variable Gyrostatic Moment," Mech. Solids. 56 (7), 1157-1166 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
7 |
Pages |
1157-1166 |
| DOI |
10.3103/S002565442107013X |
| Title |
On Solutions of the Equations of Motion of a Gyrostat with a Variable Gyrostatic Moment |
| Author(s) |
G.V. Gorr (Department of Applied Mechanics, Institute of Applied Mathematics and Mechanics, Donetsk, 84100 Ukraine, gvgorr@gmail.com)
T.V. Belokon (M. Tugan-Baranovsky National University of Economics and Trade, Donetsk, 50005 Ukraine, B.Tatyana13@mail.ru) |
| Abstract |
The problem of the motion of a gyrostat with a variable gyrostatic moment under the action
of potential and gyroscopic forces is considered. Three new solutions of the equations of motion are
obtained, which are determined by three linear invariant relations for the components of the angular
velocity vector of the gyrostat. In the case of a heavy gyrostat, a solution is found when the gyrostat
mass distribution is characterized by the Kovalevskaya and Goryachev–Chaplygin generalized conditions. The next two solutions are valid for equations of the Kirchhoff–Poisson class. One of them exists
in the case of dynamically symmetric gyrostats, and in the other solution the gyrostat mass distribution
is arbitrary. |
| Keywords |
gyrostatic moment, invariant relations, potential and gyroscopic forces, Kovalevskaya and Goryachev–Chaplygin generalized conditions |
| Received |
22 June 2020 | Revised |
12 October 2020 | Accepted |
20 October 2020 |
| Link to Fulltext |
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