 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 47, Issue 4 / 2012 | Next article >> |
| A.P. Markeev, "On the Motion of a Heavy Dynamically Symmetric Rigid Body with Vibrating Suspension Point," Mech. Solids. 47 (4), 373-379 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
4 |
Pages |
373-379 |
| DOI |
10.3103/S0025654412040012 |
| Title |
On the Motion of a Heavy Dynamically Symmetric Rigid Body with Vibrating Suspension Point |
| Author(s) |
A.P. Markeev (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, markeev@ipmnet.ru) |
| Abstract |
The motion of a dynamically symmetric rigid body in a homogeneous field of gravity is studied. One point lying on the symmetry axis of the body (the suspension point) performs high-frequency periodic or conditionally periodic vibrations of small amplitude. In the framework of approximate equations of motion obtained earlier, we find necessary and sufficient conditions for the stability of the body rotation about the vertical symmetry axis and study the existence and stability of regular precessions of the body in the coordinate system translationally moving together with the suspension point. |
| Keywords |
rigid body, vibration, precession, stability |
| References |
| 1. | A. P. Markeev,
"On the Theory of Motion of a Rigid Body with a Vibrating Suspension,"
Dokl. Ross. Akad. Nauk
427 (6), 771-775 (2009)
[Dokl. Phys. (Engl. Transl.)
54 (8), 392-396 (2009)]. |
| 2. | I. G. Malkin,
Theory of Motion Stability
(Nauka, Moscow, 1966)
[in Russian]. |
| 3. | G. K. Pozharitskii,
"On the Construction of the Liapunov Functions from the Integrals of the Equations for Perturbed Motion,"
Prikl. Mat. Mekh.
22 (2), 145-154 (1958)
[J. Appl. Math. Mech. (Engl. Transl.)
22 (2), 203-214 (1958)]. |
| 4. | N. G. Chetaev,
"On Stability of Rotation of a Rigid Body with a Single Fixed Point in the Lagrangean Case,"
Prikl. Mat. Mekh.
18 (1), 123-124 (1954)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 5. | R. Grammel,
The Gyroscope; Its Theory and Applications, Vol. 1
(Springer, Berlin, 1950; Izd-vo Inotstr. Liter., Moscow, 1952). |
| 6. | L. V. Karapetyan and V. V. Rumyantsev,
The Stability of Conservative and Dissipative Systems, in
Advances in Science and Technology. General Mechanics, Vol. 6
(VINITI, Moscow, 1983)
[in Russian]. |
|
| Received |
28 June 2010 |
| Link to Fulltext |
|
| << Previous article | Volume 47, Issue 4 / 2012 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English