 | | 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 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 |
| 1. | G. K. Suslov, Theoretical Mechanics [in Russian],
Gostekhizdat, Moscow, 1944. |
| 2. | L. D. Akulenko, D. D. Leshchenko, and F. L. Chernousko,
"Perturbed motions of a rigid body close to Lagrange's case,"
PMM [Applied Mathematics and Mechanics], Vol. 43, No. 5, pp. 771-778, 1979. |
| 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 |
06 June 2000 |
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