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IssuesArchive of Issues2005-2pp.21-32

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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 8 April 2003
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