 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V. S. Aslanov, "The motion of a rotating body in a resisting medium," Mech. Solids. 40 (2), 21-32 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
2 |
Pages |
21-32 |
| Title |
The motion of a rotating body in a resisting medium |
| Author(s) |
V. S. Aslanov (Samara) |
| Abstract |
The motion of a rotating rigid body in a resisting medium under the action of a
sinusoidal or biharmonic time-depending restoring torque and small perturbation
torques is considered in a nonlinear formulation. A justification of the
representation of the perturbations by slowly varying parameters and parameters
of small asymmetry is given. The solutions of the equations of non-perturbed
motion are presented in terms of Jacobi's elliptic functions. For the case
where the nutational torque biharmonically depends on the nutation angle, the
equations of non-perturbed motion are represented in terms of the angle-action
variables, which can be expressed in terms of complete elliptic integrals. The
averaged equations of motion of an axially symmetric body under the action of
the biharmonic torque and small damping torques are constructed. The equations
of perturbed motion of an asymmetric body are reduced to a standard
two-frequency system, and a partially averaged system is constructed. Necessary
and sufficient conditions of the stability of nonlinear resonances and those of
the Lyapunov stability of the motion in the neighborhood of a stationary point
under the action of small perturbations are obtained. A numerical example is
given to show that the stability of the resonance does not imply the stability
in the neighborhood of the stationary point, and vice versa. |
| References |
| 1. | V. A. Yaroshevskii, Motion of an Uncontrolled Body in the Atmosphere
[in Russian], Mashinostroenie, Moscow, 1978. |
| 2. | N. F. Krasnov (Editor), Aerodynamics of Rockets [in Russian], Vysshaya Shkola,
Moscow, 1968. |
| 3. | G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat,
Moscow, Leningrad, 1944. |
| 4. | V. S. Aslanov, "Nonlinear resonances in the case of uncontrolled reentry
of asymmetric spacecraft,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 30, No. 5, pp. 608-614, 1992. |
| 5. | V. S. Aslanov, "On the rotatory motion of a ballistic axially symmetric
spacecraft during its reentry,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 14, No. 4, pp. 491-497, 1976. |
| 6. | V. S. Aslanov, "The determination of the amplitude of the spatial oscillations
of a ballistic nearly-symmetric spacecraft during its reentry,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 18, No. 2, pp. 178-184, 1980. |
| 7. | V. S. Aslanov and V. V. Boiko, "Nonlinear resonant motion of an asymmetric
spacecraft in the atmosphere,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 23, No. 3, pp. 408-415, 1985. |
| 8. | V. S. Aslanov and V. M. Serov, "The rotatory motion of an axially symmetric rigid body
with the bilinear characteristic of the restoring torque,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 19-25, 1995. |
| 9. | V. M. Serov, "The rotatory motion of a dynamically symmetric rigid body
under the action of a nonlinear torque,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 26-31, 1991. |
| 10. | V. M. Volosov, "Some kinds of calculations in the theory of nonlinear
oscillations associated with averaging,"
Zh. Vychisl. Matematiki i Matem. Fiziki
[Journal of Computational Mathematics and Mathematical Physics],
Vol. 3, No. 1, pp. 3-53, 1963. |
| 11. | V. S. Aslanov and I. A. Timbai, Motion of a Rigid Body in the Generalized
Lagrange's Case [in Russian], Izd-vo SGAU, Samara, 2001. |
| 12. | L. D. Landau and E. M. Lifshits, Theoretical Physics. Volume 1. Mechanics
[in Russian], Nauka, Moscow, 1988. |
| 13. | V. S. Aslanov and S. V. Myasnikov, "Stability of nonlinear resonant modes
of motion of a spacecraft in the atmosphere,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 34, No. 6, pp. 626-632, 1996. |
| 14. | V. S. Aslanov and S. V. Myasnikov, "Analysis of nonlinear resonances
in the case of the spacecraft reentry,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 35, No. 6, pp. 659-665, 1997. |
| 15. | M. M. Khapaev, Asymptotic Methods and Stability in the Theory of Nonlinear
Oscillations [in Russian], Vysshaya Shkola, Moscow, 1988. |
| 16. | V. S. Aslanov, "Two types of nonlinear resonant motion
of an asymmetric spacecraft in the atmosphere,"
Kosmicheskie Issledovaniya [Cosmic Research], Vol. 26, No. 2, pp. 220-226, 1988. |
| 17. | L. D. Akulenko, T. A. Kozachenko, and D. D. Leshchenko,
"Perturbed rotations of a rigid body under the action of an unsteady
restoring torque depending on the nutation angle,"
in Mechanics of a Rigid Body [in Russian], No. 31, pp. 57-62,
In-t Prikl. Mat. i Mekh. NAN Ukrainy, Donetsk, 2001. |
|
| Received |
08 April 2003 |
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