 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V.D. Irtegov and T.N. Titorenko, "About Stationary Movements of the Generalized Kovalevskaya Top and Their Stability," Mech. Solids. 54 (1), 81-91 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
1 |
Pages |
81-91 |
| DOI |
10.3103/S0025654419010072 |
| Title |
About Stationary Movements of the Generalized Kovalevskaya Top and Their Stability |
| Author(s) |
V.D. Irtegov (Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences ul. Lermontova 134, Irkutsk, 664033 Russia, irteg@icc.ru)
T.N. Titorenko (Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences ul. Lermontova 134, Irkutsk, 664033 Russia) |
| Abstract |
A qualitative analysis of the equations of motion of the Kovalevskaya top in a double constant field of forces is carried out. In the framework of this study, it was established that in the case of parallel force fields, the equations of motion of the body have families of permanent rotations, in the case of orthogonal ones they have pendulum-type movements, with special orientation of force fields they have families of equilibrium positions. It is shown that the solutions belong either to one of the two invariant manifolds of codimension 2, or to their intersection. For the solutions found, necessary and sufficient conditions of Lyapunov stability are obtained. |
| Keywords |
solid, double field of forces, stationary motions, invariant manifolds, stability |
| Received |
20 June 2017 |
| Link to Fulltext |
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