 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| << Previous article | Volume 42, Issue 3 / 2007 | Next article >> |
| M. V. Shamolin, "Complete integrability of the equations of motion of a spatial pendulum in a medium flow with rotational derivatives of the torque produced by the medium taken into account," Mech. Solids. 42 (3), 491-496 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
491-496 |
| Title |
Complete integrability of the equations of motion of a spatial pendulum in a medium flow with rotational derivatives of the torque produced by the medium taken into account |
| Author(s) |
M. V. Shamolin (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, shamolin@imec.msu.ru) |
| Abstract |
We construct a nonlinearmodel of the mediumaction on a rigid body taking into account the dependence of the force arm on the reduced angular velocity of the body. In this case, the moment of the action force itself is also a function of the angle of attack. As experimental data processing for the motion of homogeneous circular cylinders in water has shown, it is necessary to take these facts into account in modeling.
Studying the model of interaction between the spatial pendulum and the medium, we found a new case of complete integrability in elementary functions. This allowed us to find several qualitative analogies between the motions of bodies that are free in the resisting environment and the oscillations of bodies partially fixed in the homogeneous flow of incoming medium. |
| References |
| 1. | M. V. Shamolin, Method for Analysis of Dynamical Systems with
Variable Dissipation in Dynamics of Solids (Izd-vo "Ekzamen",
Moscow, 2006) [in Russian]. |
| 2. | V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin,
"Mathematical Modeling in the Problem of the Deceleration of a Body
in a Resisting Medium in the Jet Flow Past this Body,"
in Research Report of the Institute of Mechanics of Moscow State
University No. 4396 (In-t Mekhaniki MGU, Moscow, 1995) [in
Russian]. |
| 3. | V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, "A Model Problem
on the Deceleration of a Body in a Resisting Medium in a Jet Flow
Past This Body," Izv. Akad. Nauk. Mekh. Zhidk. Gaza, No. 3, 23-27
(1995) [Mech. Fluids (Engl. Transl.)]. |
| 4. | S. A. Chaplygin, Selected Works (Nauka, Moscow, 1976) [in
Russian]. |
| 5. | G. S. Byushgens and R. V. Studnev,
Dynamics of Longitudinal and Lateral Motion
(Mashinostroenie, Moscow, 1969)
[in Russian]. |
| 6. | G. S. Byushgens and R. V. Studnev,
Aircraft Dynamics. Three-Dimensional Motion
(Mashinostroenie, Moscow, 1983)
[in Russian]. |
| 7. | S. A. Chaplygin,
"On the Motion of Heavy Bodies in an Incompressible Fluid,"
in Complete Works
(Izd-vo AN SSSR, Leningrad, 1933),
Vol. 1, pp. 133-150
[in Russian]. |
| 8. | M. V. Shamolin,
"On Integrability in Transcendental Functions,"
Usp. Mat. Nauk
53 (3), 209-210 (1998)
[Russ. Math. Surv.]. |
|
| Received |
29 June 2004 |
| Link to Fulltext |
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