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IssuesArchive of Issues2001-1pp.155-158

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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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