 | | 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
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| In English (Mech. Solids): | | 4760 |
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| M. V. Shamolin, "On the problem of three-dimensional deceleration of a rigid body in a resistant medium," Mech. Solids. 41 (3), 34-44 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
3 |
Pages |
34-44 |
| Title |
On the problem of three-dimensional deceleration of a rigid body in a resistant medium |
| Author(s) |
M. V. Shamolin (Moscow) |
| Abstract |
Deceleration of a rigid body in a resistant medium is considered, a type of
motion which is encountered in many practical applications. It is assumed that
a homogeneous axisymmetric body interacts with the flow only at the front
portion of its outer surface and that the interacting portion has the shape of
a flat circular disk. The experiments carried out for circular cylinders [1]
have shown that the rectilinear translational motion along
the axis of symmetry of the disk is unstable.
Under simplifying assumptions on the flow-induced forces, it is shown that the
body cannot perform finite-amplitude oscillations.
The exact analytical description of the flow-induced forces and
torques acting on the disk is not available. Therefore, the problem is
treated by its "embedding" into a wider problem class. This enables
one to obtain relatively complete qualitative description of the
body motion under the adopted model assumptions.
Despite some technical difficulties, it is possible to obtain several
particular solutions for the dynamical systems under consideration and to
construct families of phase portraits in the three-dimensional space of
quasivelocities, each family consisting of a countable set of portraits with
nonequivalent trajectories and possessing different nonlinear qualitative
properties. |
| References |
| 1. | V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin,
"Model problem of deceleration of a rigid body in a resistant medium
under jet flow," Izv. AN. Mekhanika Zhidkosti i Gaza [Fluid Dynamics],
No. 3, pp. 23-27, 1995. |
| 2. | S. A. Chaplygin, Selected Works [in Russian], Nauka,
Moscow, 1976. |
| 3. | M. I. Gurevich, Theory of Jets of an Ideal Fluid [in
Russian], Nauka, Moscow, 1970. |
| 4. | B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov,
Introduction to the Motion of a Rigid Body in a
Resistant Medium [in Russian], Izd-vo MGU, Moscow, 1986. |
| 5. | S. A. Chaplygin, "On the motion of heavy bodies in an incompressible
fluid," in S. A. Chaplygin, Collected Works [in Russian], Izd-vo AN SSSR,
Leningrad, 1933, Vol. 1, pp. 133-135. |
| 6. | M. V. Shamolin, "Introduction to the problem of
deceleration of a body in a resistant medium and a new two-parameter
family of phase portraits," Vestnik MGU [Bulletin of the Moscow
State University], Ser. 1, No. 4, pp. 57-69, 1996. |
| 7. | M. V. Shamolin, "A new two-parameter family of phase portraits in the
problem of the motion of a body in a medium," Doklady RAN, Vol. 337, No. 5,
pp. 611-614, 1994. |
| 8. | M. V. Shamolin, "Variety of types of phase portraits in the dynamics
of a rigid body interacting with a resistant medium," Doklady RAN, Vol. 349,
No. 2, pp. 193-197, 1996. |
| 9. | M. V. Shamolin, "Some classes of particular solutions in dynamics
of a rigid body interacting with a medium,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 178-189, 1999. |
| 10. | M. V. Shamolin, "Poincaré's spatial topographic systems and
comparison systems," Uspekhi Matematicheskikh Nauk, Vol. 52, No. 3,
pp. 177-178, 1997. |
|
| Received |
29 June 2002 |
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