 | | 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
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 50, Issue 3 / 2015 | Next article >> |
| O.S. Volkova, "Motion of a Heavy Gyrostat with Variable Gyrostatic Moment in the Generalized Steklov Case," Mech. Solids. 50 (3), 233-244 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
3 |
Pages |
233-244 |
| DOI |
10.3103/S0025654415030012 |
| Title |
Motion of a Heavy Gyrostat with Variable Gyrostatic Moment in the Generalized Steklov Case |
| Author(s) |
O.S. Volkova (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. Rozy Luksemburg 74, Donetsk, 83114 Ukraine, volkova@iamm.ac.donetsk.ua, vo-va-o@yand) |
| Abstract |
Several families of isoconic motions of a heavy nonautonomous gyrostat with a fixed point are analyzed. Assuming that the conditions for the existence of a generalized Steklov solution are satisfied, we indicate the explicit time dependence of the main variables and analytically study the fixed hodographs of the angular velocity ω, the total angular momentum K of the system, and the center of mass position vector. The time dependence of the angle between K and ω is written out and examined. We obtain restrictions on the values of the nutation and proper rotation angles. |
| Keywords |
gyrostat, variable gyrostatic moment, particular solution of the equations of motion |
| References |
| 1. | V. A. Steklov,
"A New Particular Solution of Differential Equations of Motion of a Heavy Rigid Body with a Fixed Point,"
Trudy Otd. Fiz. Nauk Obshch. Lubit. Estestvozn.
10 (1), 1-3 (1899). |
| 2. | P. V. Kharlamov, "Gyrostats," Dokl. Akad. Nauk Ukr. SSR. Ser. A.
Fiz. Mat. Tekhn. Nauki, No. 9, 38-41 (1988). |
| 3. | T. Levi-Civita and U. Amaldi,
Lezioni di Meccanica Razionale, Vol. 2, Part 2
(Zabiuchelli, Bologna, 1927; Izdat. Inostr. Lit., Moscow 1951). |
| 4. | E. I. Druzhinin, "The Permanent Rotations of a Balanced
Nonautonomous Gyrostat," Prikl. Mat. Mekh. 63 (5),
875-876 (1999) [J. Appl. Math. Mech. (Engl. Transl.) 63. (5), 825-826 (1999)]. |
| 5. | L. M. Kovaleva,
"Investigation of Permanent Rotations of a Rigid Body with a Fixed Point
Carrying One- and Two-Degree Gyros,"
in XXII Yugoslav Conf. on Theoret. and Appl. Mechanics.. (Vrnjaska Banja, 1997),
pp. 61-64. |
| 6. | O. S. Volkova and I. N. Gashenenko, "Exact Solutions of Equations
of a Gyrostat Motion about a Fixed Point," in Contemporary
Problems of Mathematics, Mechanics, and Informatics (Apostrof, Kharkov, 2011), pp. 74-84. |
| 7. | O. S. Volkova, Several Classes of Motion of a Heavy Gyrostat with Variable Gyrostatic Moment, Abstract of Candidate's Dissertation in Mathematics and Physics (IPMM NAN Ukraine, Donetsk,
2010) [in Russian]. |
| 8. | O. S. Volkova, "Invariant Relation between the Equations of Motion
of a Heavy Gyrostat Whose Center of Mass Lies in the Principal
Plane," Mekhanika Tverdogo Tela (Izdat. NAN Ukraine), No. 42,
76-83 (2012). |
| 9. | O. S. Volkova, "An Analog of the Steklov Problem Solution in the
Problem of Motion of a Heavy Gyrostat with Variable Gyrostatic
Moment," Dokl. Nats. Akad. Nauk Ukraine, No. 9, 65-70 (2013). |
| 10. | P. V. Kharlamov,
Lectures in Dynamics of Solids. (Izdat. Novosibirsk Univ., Novosibirsk, 1965)
[in Russian]. |
| 11. | R. Fabbri,
"Sur les Rotations Isoconiques,"
C.r. hebdomadaires des seances de l'Academie des Sciences
198, 1746-1747 (1934). |
| 12. | P. Field,
"On the Unsymmetrical Top,"
Acta Math.
56 (1), 355-362 (1931). |
| 13. | R. Fabbri, "Sopra un particolare movimento di un solido pesante
intorno a un punto fisso," Rend. Acc. Naz. dei Lincei, Ser. 6,
No. 19, 38-41 (1934). |
| 14. | I. N. Gashenenko, G. B. Gorr, and A. M. Kovalev,
Classical Problems of Dynamics of Solids. (Naukova Dumka, Kiev, 2012). |
| 15. | P. V. Kharlamov and E. K. Sergeev,
"Construction of Complete Solution of a Problem of Dynamics of Solids,"
Mekhanika Tverdogo Tela (Izdat. NAN Ukraine),
No. 14, 33-38 (1982). |
| 16. | E. I. Kharlamova and G. V. Mozalevskaya, "Study of the Solution to
the V. A. Steklov Equations of Motion of a Body with a Fixed Point," in Mathematics (Naukova Dumka, Kiev, 1968),
No. 5, pp. 194-202. |
| 17. | A. P. Markeev,
"Motion of a Rigid Body with a Single Fixed Point in the Steklov Case,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 20-33 (2005)
[Mech. Solids (Engl. Transl.)
40 (1), 14-25 (2005)]. |
| 18. | A. A. Savelov,
Plane Curves: Systematics, Properties, Applications,
Ed. by A. P. Norden
(Fizmatgiz, Moscow, 1960)
[in Russian]. |
|
| Received |
02 August 2013 |
| Link to Fulltext |
|
| << Previous article | Volume 50, Issue 3 / 2015 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English