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IssuesArchive of Issues2003-1pp.13-23

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V. S. Aslanov and I. A. Timbai, "Action-angle canonical variables for the motion of a rigid body under the action of a biharmonic torque," Mech. Solids. 38 (1), 13-23 (2003)
Year 2003 Volume 38 Number 1 Pages 13-23
Title Action-angle canonical variables for the motion of a rigid body under the action of a biharmonic torque
Author(s) V. S. Aslanov (Samara)
I. A. Timbai (Samara)
Abstract The motion of a nearly dynamically symmetric rigid body under the action of the nutation torque and a small perturbation torque is considered. The nutation torque is assumed to be represented by an odd Fourier series in terms of the nutation angle, with the coefficients slowly changing in time. For the case where the nutation torque is a biharmonic function of the nutation angle, the equations of the unperturbed motion are written with respect to the action-angle variables expressed in terms of complete elliptic integrals. All possible particular cases corresponding to various domains of the system phase portrait are considered. The relationship between the canonical action-angle variables and Eulerian variables is established.
References
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3.  V. S. Aslanov, "Nonlinear resonances during the uncontrolled reentry of an asymmetric spacecraft," Kosmicheskie Issledovaniya, Vol. 30, No. 5, pp. 608-614, 1992.
4.  A. V. Bobylev and V. A. Yaroshevskii, "Evaluation of the conditions for the resonant rotation capture of an uncontrolled body during the reentry," Kosmicheskie Issledovaniya, Vol. 37, No. 5, pp. 515-523, 1999.
5.  V. M. Serov, "Rotation of a dynamically asymmetric rigid body under the action of a nonlinear torque," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 26-31, 1991.
6.  V. S. Aslanov and I. A. Timbai, "The action integral in the motion of a rigid body in Lagrange's generalized case," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 9-17, 1998.
7.  Yu. A. Sadov, "Angle-action variables in Euler-Poinsot problem," PMM [Applied Mathematics and Mechanics], Vol. 34, No. 5, pp. 962-964, 1970.
8.  I. M. Aksenenkova, "Classical action-angle variables in the problem of Lagrange's top," Vestnik MGU. Ser. 1. Matematika, Mekhanika [Bulletin of the Moscow State University], No. 1, pp. 86-90, 1981.
9.  V. G. Demin and L. I. Konkina, New Methods in Dynamics of a Rigid Body [in Russian], Ilim, Frunze, 1989.
10.  Yu. A. Arkhangel'skii, Analytical Dynamics of a Rigid Body [in Russian], Nauka, Moscow, 1977.
11.  G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers [Russian translation], Nauka, Moscow, 1984.
12.  F. R. Gantmakher, Lectures on Analytical Mechanics [in Russian], Fizmatgiz, Moscow, 1960.
Received 6 June 2000
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