 | | 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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| M. V. Shamolin, "Stability of motion of a rigid body spinned about its longitudinal axis in a resisting medium," Mech. Solids. 36 (1), 155-158 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
1 |
Pages |
155-158 |
| Title |
Stability of motion of a rigid body spinned about its longitudinal axis in a resisting medium |
| Author(s) |
M. V. Shamolin (Moscow) |
| Abstract |
Free deceleration of a dynamically symmetric rigid body
under jet flow conditions [1-3] is studied. The basic hypothesis
underlying the construction of the dynamical model is that
the flow is quasi-steady [1, 4]. It is assumed that the body
interacts with the medium only by part of its surface
having the shape of a circular disk. The rectilinear deceleration
of such a body in the absence of its proper rotation is unstable
with respect to the angle of attack and the angular velocity.
It is shown in the present paper that an increase in the speed
of rotation of the body about its longitudinal axis leads
to the appearance of a two-dimensional plane attractor in
the phase space of the dynamical equations. |
| References |
| 1. | S. A. Chaplygin, Selected Works [in Russian], Nauka,
Moscow, 1976. |
| 2. | M. I. Gurevich, Theory of Jets in an Ideal Fluid [in Russian],
Moscow, Nauka, 1979. |
| 3. | A. A. Il'yushin, Continuum Mechanics [in Russian],
Izd-vo MGU, Moscow, 1990. |
| 4. | B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov,
Introduction to the Theory of Motion of a Body in a Resisting
Medium [in Russian], Izd-vo MGU, Moscow, 1986. |
| 5. | M. V. Shamolin, "On the integrable case in the 3D dynamics
of a solid interacting with a medium,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 65-68, 1997. |
| 6. | M. V. Shamolin, "New Jacobi integrable cases in the dynamics
of a rigid body interacting with a medium,"
Doklady AN, Vol. 364, No. 5, pp. 627-629, 1999. |
| 7. | S. A. Chaplygin, An Approximate Method for Solving
Gas Jet Problems. Volume 2 [in Russian], pp. 84-87, Izd-vo AN SSSR,
Leningrad, 1953. |
| 8. | G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal
and Lateral Motion [in Russian], Mashinostroenie, Moscow, 1969. |
| 9. | G. S. Byushgens and R. V. Studnev, Aircraft Dynamics.
Spatial Motion [in Russian], Mashinostroenie, Moscow, 1988. |
| 10. | M. V. Shamolin, "Poincaré's 3D topographic systems
and reference systems," Uspekhi Matemaicheskikh Nauk [Advances
in Mathematics], Vol. 52, No. 3, pp. 177-178, 1997. |
| 11. | G. K. Suslov, Theoretical Mechanics [in Russian],
Gostekhizdat, Moscow, 1946. |
|
| Received |
12 October 2000 |
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