 | | 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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| G.V. Gorr and A.V. Maznev, "On a Class of Motions of a Zhukovskii Gyrostat with Variable Gyrostatic Moment," Mech. Solids. 48 (3), 237-242 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
3 |
Pages |
237-242 |
| DOI |
10.3103/S0025654413030011 |
| Title |
On a Class of Motions of a Zhukovskii Gyrostat with Variable Gyrostatic Moment |
| Author(s) |
G.V. Gorr (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Rozy Luksemburg 74, Donetsk, 83114 Ukraine, gvgorr@gmail.com)
A.V. Maznev (Donetsk National University, Universitetskaya 24, Donetsk, 83001 Ukraine, maznev_av@rambler.ru) |
| Abstract |
The paper deals with the problem of Zhukovskii gyrostat motions in the case of a constant angle between the gyrostat invariable axis and the gyrostat angular momentum vector. It is assumed that the gyrostatic moment depends on time. The obtained conditions on the gyrostat parameters and the expression for the gyrostatic moment characterize a new solution of the Zhukovskii equations with variable gyrostatic moment. We prove that it describes semiregular precession of the first type with respect to the angular momentum vector. |
| Keywords |
gyrostat, gyrostatic moment, invariant relation, semiregular precession |
| References |
| 1. | N. E. Zhukovskii,
"On the Motion of a Solid Filled with a Homogeneous Dropping Liquid,"
in Complete Works, Vol. 2
(OGIZ, Moscow-Leningrad, 1949),
pp. 152-309.
[in Russian]. |
| 2. | Yu. P. Barkhalev and G. V. Gorr,
"Classification of the Motions of a Zhukovskii Gyrostat,"
Prikl. Mekh.
20 (8), 104-111 (1984)
[Int. Appl. Mekh. (Engl. Transl.)
20 (8), 770-776 (1984)]. |
| 3. | P. V. Kharlamov,
"On Equations of Motion of a System of Solids,"
in Mechanics of Solids, No. 4
(Naukova Dumka, Kiev, 1972),
pp. 52-73
[in Russian]. |
| 4. | G. V. Gorr,
"Precessional Motions in Rigid Body Dynamics and the Dynamics of Systems of Coupled Rigid Bodies,"
Prikl. Mat. Mekh.
67 (4), 573-587 (2003)
[J. Appl. Math. Mech. (Engl. Transl.)
67 (4), 511-523 (2003)]. |
| 5. | P. V. Kharlamov,
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Prikl. Mat. Mekh.
28 (3), 502-507 (1964)
[J. Appl. Math. Mech. (Engl. Transl.)
28 (3), 515-521 (1964)]. |
| 6. | E. I. Kharlamova,
"On Inertial Motion of a Gyrostat,"
in Mechanics of Solids, No. 10
(Naukova Dumka, Kiev, 1978),
pp. 34-40
[in Russian]. |
| 7. | L. M. Kovaleva,
"A Special Case of Inertial Motion of a Gyrostat. Separating Motions"
in Mechanics of Solids, No. 10
(Naukova Dumka, Kiev, 1978),
pp. 41-45
[in Russian]. |
| 8. | D. N. Kravchuk,
"Geometric Interpretation of a Class of Inertial Motions of a Gyrostat,"
in Mechanics of Solids, No. 18
(Naukova Dumka, Kiev, 1986),
pp. 15-22
[in Russian]. |
| 9. | V. Volterra,
"Sur la Théorie des Variations des Latitudes,"
Acta Math.
22, 201-358 (1899). |
| 10. | E. I. Druzhinin,
"The Permanent Rotations of a Balanced Non-Autonomous Gyrostat,"
Prikl. Mat. Mekh.
63 (5), 875-876 (1999)
[J. Appl. Math. Mech. (Engl. Transl.)
63 (5), 825-826 (1999)]. |
|
| Received |
03 March 2011 |
| Link to Fulltext |
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