 | | 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
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| In English (Mech. Solids): | | 4810 |
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| M. V. Deryabin, "On the stability of uniformly accelerated rotations of a heavy rigid body in an ideal fluid," Mech. Solids. 37 (5), 23-26 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
5 |
Pages |
23-26 |
| Title |
On the stability of uniformly accelerated rotations of a heavy rigid body in an ideal fluid |
| Author(s) |
M. V. Deryabin (Moscow) |
| Abstract |
The motion of a heavy rigid body in an unbounded volume
of an ideal incompressible fluid which performs irrotational
motion and is in the state of rest at infinity was considered
by S. A. Chaplygin [1] and V. A. Steklov [2]. These authors
have found particular solutions of the equations of motion
of a rigid body in the cases where this body has a plane
of symmetry or an axis of screw symmetry (in the latter case
the shape of the body is invariant to the rotation by
an angle of 180° about this axis [1]) and formulated
the problem of stability of the respective motions. For a body
having three mutually orthogonal planes of symmetry, this
problem has been solved in [3]. In the present paper, we
consider the case where the body has three mutually orthogonal
axes of screw symmetry and investigate the first-approximation
stability of uniformly accelerated rotations of such a body
about its axes of symmetry. |
| References |
| 1. | S. A. Chaplygin, "On the motion of heavy bodies in
an incompressible fluid," in S. A. Chaplygin, Complete Works.
Volume 1 [in Russian], pp. 133-150, Izd-vo AN SSSR, Moscow, 1933. |
| 2. | V. A. Steklov, "On the motion of a heavy body in a fluid,"
Soobshcheniya Kharkovs. Mashinostroit. Ob-va,
Ser. 2, Vol. 2, No. 5-6, 1889. |
| 3. | V. V. Kozlov, "On the stability of equilibria in
a non-stationary force field," PMM [Applied Mathematics
and Mechanics], Vol. 55, No. 1, pp. 12-19, 1991. |
| 4. | G. Kirchhoff, "Uber die Bewengung eines
Rotationkorpers in einer Flussigkeit," J. Reine und Angewandte
Math., Bd. 71, S 237-262, 1870. |
| 5. | G. Lamb, Hydrodynamics [Russian translation],
Gostekhizdat, Moscow, Leningrad, 1947. |
| 6. | E. A. Coddington and N. Levinson,
Theory of Ordinary Differential Equations [Russian translations],
Izd-vo Inostr. Lit-ry, Moscow, 1958. |
| 7. | V. V. Kozlov, "On the fall of a heavy rigid body in an ideal
fluid," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 5, pp. 10-17, 1989. |
|
| Received |
04 October 1999 |
| << Previous article | Volume 37, Issue 5 / 2002 | Next article >> |
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