 | | 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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| << Previous article | Volume 48, Issue 6 / 2013 | Next article >> |
| S.A. Agafonov and T.V. Muratova, "Onset of Chaotic Motion in a Gyroscopic System," Mech. Solids. 48 (6), 620-622 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
6 |
Pages |
620-622 |
| DOI |
10.3103/S0025654413060046 |
| Title |
Onset of Chaotic Motion in a Gyroscopic System |
| Author(s) |
S.A. Agafonov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005 Russia, seragav@yandex.ru)
T.V. Muratova (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005 Russia, tamura@bk.ru) |
| Abstract |
We study forced vibrations of a gimbal gyro occurring if the inner ring is subjected to a perturbing torque that is the sum of the viscous friction torque and a periodic small-amplitude torque. In the absence of the perturbing torque, there exist two steady-state motions of the gimbal gyro, in which the gimbal rings are either orthogonal or coincide. These motions are respectively stable and unstable. We obtain an equation for the unperturbed system, whose separatrix passes through hyperbolic points. The distance between these points (the Melnikov distance) is calculated to find a condition for the intersection of the separatrices of the perturbed system.
We find a domain in the parameter space where the distance changes sign, which indicates the onset of chaotic motion. |
| Keywords |
gimbal gyro, perturbing torque, Routh function, hyperbolic and elliptic points, homoclinic solution, conditions for the intersection of separatrices in the perturbed system, local criterion for the onset of chaotic motion |
| References |
| 1. | V. K. Melnikov, "On the Stability of the Center for Time-Periodic
Perturbations," Trudy Moskov. Mat. Obshch., 12, 3-52
(1963) [Trans. Moscow Math. Soc. (Engl. Transl.) 12, 1-53
(1963)]. |
| 2. | S. Wigglings,
Global Bifurcations and Chaos
(Springer, New York-Heidelberg-Berlin, 1988). |
| 3. | A. Yu. Ishlinskii,
Mechanics of Gyroscopic Systems
(Izd-vo AN SSSR, Moscow, 1963)
[in Russian]. |
|
| Received |
29 November 2011 |
| Link to Fulltext |
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