 | | 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
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| In English (Mech. Solids): | | 4760 |
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| A. M. Pil'kevich, V. A. Storozhenko, and M. E. Temchenko, "On the stability of the steady-state motion of a rigid body rotating on a short string," Mech. Solids. 36 (6), 25-42 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
6 |
Pages |
25-42 |
| Title |
On the stability of the steady-state motion of a rigid body rotating on a short string |
| Author(s) |
A. M. Pil'kevich (Kiev)
V. A. Storozhenko (Kiev)
M. E. Temchenko (Kiev) |
| Abstract |
One of the steady-state modes of motion of an axisymmetric rigid
body suspended on a string is investigated. This mode occurs when
the linear dimensions of the body are commensurable with the length
of the string and satisfy the Bugaenko-Veligotskii condition [1].
In this case, the stability analysis is reduced to the investigation
of a system with an even number of negative Poincaré exponents (the
gyroscopic stabilization). The investigation involves
graphical-analytical methods permitting one to construct stability
zones in the space of parameters. |
| References |
| 1. | G. O. Bugaenko and G. G. Veligotskii, "Dynamic equilibrium
modes for one mechanical system," Nauk. Zap. Cherkas'k Ped. In-tu,
Vol. 17, pp. 21-37, 1963. |
| 2. | A. Yu. Ishlinskii, V. A. Storozhenko, and M. E. Temchenko,
Rotation of a Rigid Body on a String and Related Problems [in Russian],
Nauka, Moscow, 1991. |
| 3. | A. M. Pil'kevich, V. A. Storozhenko, and M. E. Temchenko,
Stability of One of the Steady-state Modes of Motion of a Rigid Body
Suspended on a Short String. Preprint No. 2 [in Russian], IM NANU,
Kiev, 1999. |
| . | 4. A. I. Lur'e, Analytical Mechanics [in Russian],
Fizmatgiz, Moscow, 1961. |
| 5. | M. E. Temchenko, "On the stability of one of the equilibrium
positions of one mechanical system," Doklady AN SSSR, Vol. 117, No. 1,
pp. 50-52, 1957. |
| 6. | V. N. Skimel', "To problems of stability of motion of a heavy
rigid body with a fixed point," PMM [Applied Mathematics and Mechanics],
Vol. 20, No, 1, pp. 130-132, 1956. |
| 7. | N. G. Chetaev, Stability of Motion. Works on Analytical Mechanics
[in Russian], Izd-vo AN SSSR, Moscow, 1962. |
| 8. | V. A. Storozhenko and B. M. Shuman, Investigation of the Gyroscopic
Stability of One of the Steady-state Modes of Motion of a Rigid Body on
a String. Preprint No. 91-32 [in Russian], In-t Matematiki AN USSR, Kiev,
1991. |
| 9. | A. Yu. Ishlinskii and M. E. Temchenko, "On the stability of the rotation
of a rigid body with an ellipsoidal cavity completely filled with an ideal
incompressible fluid on a string," PMM [Applied Mathematics and Mechanics],
Vol. 30, No, 1, pp. 30-41, 1966. |
| 10. | M. E. Temchenko, "On the investigation of stability criteria
for the motion of a rigid body and a top with an ellipsoidal cavity
filled with a fluid on a string," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 1, pp. 26-31, 1969. |
| 11. | N. N. Meiman, "Some issues of the arrangement of zeros
of polynomials," Uspekhi Matemeticheskikh Nauk [Advances in Mathematics],
Vol. 4, No. 6, pp. 154-158, 1949. |
|
| Received |
26 June 1999 |
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