 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| B.I. Konosevich and Yu.B. Konosevich, "Stability of Stationary Motions of a Gimbal Gyro with an Electric Motor," Mech. Solids. 48 (3), 285-297 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
3 |
Pages |
285-297 |
| DOI |
10.3103/S0025654413030059 |
| Title |
Stability of Stationary Motions of a Gimbal Gyro with an Electric Motor |
| Author(s) |
B.I. Konosevich (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Rozy Luksemburg 74, Donetsk, 83114 Ukraine, konos@iamm.ac.donetsk.ua)
Yu.B. Konosevich (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Rozy Luksemburg 74, Donetsk, 83114 Ukraine) |
| Abstract |
A gimbal gyro on an immovable base in the gravity field and with vertical outer suspension axis is considered. The rotor is driven by an asynchronous or synchronous electric motor, and there is no friction or any controlling torques on the suspension axes. Such a system has a family of steady-state motions (regular precessions and the rotor uniform rotations). It is shown that a necessary and sufficient condition for stability of the steady-state motions with respect to generalized velocities and the angle of rotation of the inner gimbal frame is the existence of an isolated minimum of the reduced potential energy with respect to the angle of rotation of the inner frame. |
| Keywords |
gimbal gyro, steady-state motion, stability, asynchronous or synchronous electric motor |
| References |
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| 2. | K. Magnus,
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22 (2), 173-178 (1958)
[J. Appl. Math. Mech. (Engl. Transl.)
22 (2), 237-243 (1958)]. |
| 3. | V. V. Rumiantsev,
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Prikl. Mat. Mekh.
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[in Russian]. |
| 8. | V. V. Krementulo,
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[in Russian] |
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Stability by Lyapunov's Direct Method
(Academic Press, New York, London, 1961; Mir, Moscow, 1964). |
|
| Received |
01 October 2010 |
| Link to Fulltext |
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