 | | 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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| Yu. M. Zabolotnov and V. V. Lyubimov, "Secondary resonance effects in the rotation of a rigid body about a fixed point," Mech. Solids. 37 (1), 39-46 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
39-46 |
| Title |
Secondary resonance effects in the rotation of a rigid body about a fixed point |
| Author(s) |
Yu. M. Zabolotnov (Samara)
V. V. Lyubimov (Samara) |
| Abstract |
The motion of a dynamically symmetric heavy rigid body about
a fixed point in the neighborhood of a statically stable
equilibrium is considered. The body is acted upon by
a nonlinear restoring torque and a perturbation torque
the vector of which is constant in the body-associated coordinate
frame. The center of mass of the body is shifted by
a small distance from the axis of dynamic symmetry.
For the nonlinear restoring torque approximated by a polynomial
of degree 3 in the nutation angle, the resonances occurring
in this problem are established by means of the method of averaging.
The construction of the second approximation of the method
of averaging permitted us to analyze all possible motions and
establish secondary resonance effects [1] determining the evolution
of the system on nonresonant segments of the motion of a rigid body.
Numerical examples are presented to illustrate typical cases of
the motion of the body in the problem under consideration. |
| References |
| 1. | Yu. A. Sadov,
"Secondary resonance effects in mechanical systems,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 20-24, 1990. |
| 2. | A. H. Nayfeh and V. Sarik,
"Analysis of asymmetric rotating bodies with nonlinear
aerodynamic characteristics," Raketnaya Tekhnika i Kosmonavtika,
Vol. 10, No. 8, pp. 38-47, 1972. |
| 3. | Yu. M. Zabolotnov, "Asymptotic analysis of quasilinear
equations governing the motion of a spacecraft with small asymmetry
in the atmosphere,"
Kosmicheskie Issledovaniya [Space Research],
Vol. 31, No. 6, pp. 39-50, 1993. |
| 4. | N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics
[in Russian], Nauka, Moscow, 1981. |
| 5. | Yu. A. Sadov,
"Rapid rotation of a satellite with a magnetic damper. Part 4:
Dissipative evolution. Resonance effects,"
Kosmicheskie Issledovaniya [Space Research],
Vol. 24, No. 4, pp. 553-563, 1986. |
|
| Received |
20 September 1999 |
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