 | | 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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| A.A. Kosov, "On the Stability of Stationary Solutions of the Equations of Motion of the Goryachev–Sretensky Gyrostat," Mech. Solids. 58 (6), 1986-1997 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
6 |
Pages |
1986-1997 |
| DOI |
10.3103/S0025654423600460 |
| Title |
On the Stability of Stationary Solutions of the Equations of Motion of the Goryachev–Sretensky Gyrostat |
| Author(s) |
A.A. Kosov (Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, 664033 Russia, kosov_idstu@mail.ru) |
| Abstract |
The equations of motion of the Goryachev-Sretensky gyrostat are studied. It has been established that one component of the angular velocity vector oscillates with zero average value on all solutions outside the set of zero level of the area integral. All stationary solutions are found, including two states of rest and two parametric families of permanent rotations. Using Chetaev's method of integral connectives, sufficient conditions for the stability of stationary solutions are obtained. Based on the analysis of the roots of the characteristic equation, instability conditions were obtained. The possibility of gyroscopic stabilization due to the moment of circular-gyroscopic forces under certain conditions has been established. |
| Keywords |
Goryachev-Sretensky gyrostat, partial and general integrals, stationary solutions, stability |
| Received |
25 August 2022 | Revised |
11 March 2023 | Accepted |
23 March 2023 |
| Link to Fulltext |
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