 | | 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: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| A.A. Kosov, "On Analogues of the Hess Case for a Gyrostat under the Action of the Moment of Gyroscopic and Circular Forces," Mech. Solids. 57 (8), 1848-1861 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
1848-1861 |
| DOI |
10.3103/S0025654422080192 |
| Title |
On Analogues of the Hess Case for a Gyrostat under the Action of the Moment of Gyroscopic and Circular Forces |
| 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 article considers the equations of motion of a gyrostat around a fixed point affected by
the moment of potential, gyroscopic and circular forces. Six analogues of the Hess case are distinguished, in which the system of equations of motion has a linear particular integral. An additional general integral is found for two cases. It is established that the component of the angular velocity vector,
which is not included in the Hess integral, oscillates with zero mean on all solutions outside the Hess
set. Three types of stationary solutions are given, and sufficient conditions for their stability are
obtained by the Chetaev method of integral connectives. |
| Keywords |
gyrostat, gyroscopic and circular forces, analogues of the Hess case, particular and general integrals, stationary solutions, stability |
| Received |
29 May 2022 | Revised |
30 August 2022 | Accepted |
30 August 2022 |
| Link to Fulltext |
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