 | | 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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| << Previous article | Volume 36, Issue 4 / 2001 | Next article >> |
| S. A. Agafonov, "Two problems of stabilization of the steady-state motion of an unbalanced gyroscope in gimbals," Mech. Solids. 36 (4), 7-11 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
4 |
Pages |
7-11 |
| Title |
Two problems of stabilization of the steady-state motion of an unbalanced gyroscope in gimbals |
| Author(s) |
S. A. Agafonov (Moscow) |
| Abstract |
The solution of two problems of stabilization of the steady-state
motion of an unbalanced gyroscope in gimbals is given. We consider
a mechanical system able to perform the steady-state motion in which
the planes of the rings are orthogonal, the gyroscope rotates at
constant speed, and its center of mass lies above the point of
intersection of the gimbals axes. The stability of the steady-state
motion is achieved due to the gyroscopic stabilization. However,
according
to Kelvin-Tait theorems, forces of full dissipation destroy
the gyroscopic stabilization. This fact gives rise to the problem
of stabilization of the steady-state motion by means of external
forces. In the first problem, the stabilization is implemented
by the external nonconservative torque that depends on the angles
of rotation of the rings and is applied to the gimbals axes. A Lyapunov
function is constructed to obtain the condition of stabilization
of the steady-state motion to the asymptotic stability, and
the attraction region is evaluated. In the second problem,
the steady state motion is stabilized
by the parametric excitation implemented by means of
the vertical vibration of the base in accordance with a fairly
general law. A stabilization condition expressed in terms of
the integral characteristics of the parametric excitation is
found. The case of the balanced gyroscope in gimbals was considered
in [1]. |
| References |
| 1. | S. A. Agafonov, "Stability of steady-state motion
of a gyroscope in gimbals subjected to a disturbing torque,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 3-8, 1996. |
| 2. | V. V. Rumyantsev, "On the stability of motion of a gyroscope
in gimbals," PMM [Applied Mathematics and Mechanics], Vol. 22,
No. 4, pp. 499-503, 1958. |
| 3. | S. A. Agafonov, "On the stability of motion of nonconservative
mechanical systems," PMM [Applied Mathematics and Mechanics], Vol. 56,
No. 2, pp. 212-217, 1992. |
| 4. | S. A. Agafonov, "Stabilization of motion of nonconservative
systems by parametric excitation,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 199-202, 1998. |
| 5. | V. N.Koshlyakov, "On structural transformations of dynamical
systems with gyroscopic forces,"
PMM [Applied Mathematics and Mechanics], Vol. 61,
No. 5, pp. 774-780, 1997. |
|
| Received |
26 February 1999 |
| << Previous article | Volume 36, Issue 4 / 2001 | Next article >> |
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