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IssuesArchive of Issues2006-4pp.29-39

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V. S. Aslanov and A. V. Doroshin, "Two cases of motion of an unbalanced gyrostat," Mech. Solids. 41 (4), 29-39 (2006)
Year 2006 Volume 41 Number 4 Pages 29-39
Title Two cases of motion of an unbalanced gyrostat
Author(s) V. S. Aslanov (Samara)
A. V. Doroshin (Samara)
Abstract We consider two cases of motion of an unbalanced gyrostat, namely, a heavy dynamically symmetric gyrostat with arbitrary internal interaction moment and a free gyrostat with internal moment of special form. For the heavy gyrostat, we obtain general solutions of the equations of motion in terms of Jacobi elliptic functions and study the mode of "lunar" motion. We consider the motion of the free gyrostat whose rotor rotates around the principal axis of inertia of the platform (this axis corresponds to the maximum moment of inertia) under the action of a moment of special form. In this case, the solutions of the dynamic equations of motion are also found in terms of elliptic functions admitting the subsequent solution of the Darboux problem. The solutions obtained can be used in applied problems of space flight mechanics, in particular, in problems of spacecraft reentry and in the description of the motion and realignment of a satellite-gyrostat in space.
References
1.  N. E. Zhukovskii, Motions of a Solid with Cavities Filled with a Homogeneous Dropping Liquid [in Russian], Gostekhizdat, Moscow-Leningrad, 1931.
2.  N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Solid with Cavities Filled with Fluid [in Russian], Nauka, Moscow, 1965.
3.  V. V. Rumyantsev, "On stability of motions of gyrostats," PMM [Applied Mathematics and Mechanics], Vol. 25, No. 1, pp. 9-16, 1961.
4.  J. Wittenburg, Dynamics of Systems of Rigid Bodies [Russian translation], Nauka, Moscow, 1980.
5.  P. V. Kharlamov, Lectures on Dynamics of Solids. Part 1 [in Russian], , Novosibirsk Univ., Novosibirsk, 1965.
6.  G. V. Gorr, A. A. Ilyukhin, A. M. Kovalev, and A. Ya. Savchenko, Nonlinear Analysis of Behavior of Mechanical Systems [in Russian], Naukova Dumka, Kiev, 1984.
7.  E. I. Kharlamova and G. V. Gorr, "On nutation-free motions of a rigid body with a fixed point," in Mekh. Tverd. Tela, No. 8, pp. 23-31, Naukova Dumka, Kiev, 1976.
8.  V. N. Koshlyakov, Problems in Dynamics of Rigid Bodies and in Applied Theory of Gyroscopes [in Russian], Nauka, Moscow, 1985.
9.  V. V. Strygin and V. A. Sobolev, "Influence of geometric and kinetic parameters and the energy dissipation on the stability of orientation of satellites with double rotation," Kosmicheskie Issledovaniya, Vol. 14, No. 3, pp. 366-371, 1976.
10.  V. V. Strygin and V. A. Sobolev, Separation of Motions by the Method of Integral Manifolds [in Russian], Nauka, Moscow, 1988.
11.  V. Volterra, "Sur la theorie des variations des latitudes," Acta Math., Vol. 22, pp. 201-358, 1899.
12.  V. V. Beletskii (Editor), Problems of Stabilization of Compound Satellites [in Russian], Mir, Moscow, 1975.
13.  V. V. Rumyantsev, "On stability of rotation of a heavy gyrostat on the horizontal plane," Izv. AN SSSR MTT [Mechanics of Solids], No. 4, pp. 11-21, 1980.
14.  E. A. Ivin, "Separation of variables in the problem of gyrostat motion," Vestnik MGU [Bulletin of the Moscow University]. Ser. I Mat. Mekh., No. 3, pp. 69-72, 1985.
15.  L. N. Oreshkina, "Combination of two problems of dynamics of rigid bodies," Izv. AN SSSR MTT [Mechanics of Solids], No. 5, pp. 36-43, 1986.
16.  Kh. M. Yakh'ya, "New integrable cases of the problem of gyrostat motion," MGU [Bulletin of the Moscow University]. Ser. I Mat. Mekh., No. 4, pp. 88-90, 1987.
17.  A. I. Neischtadt and M. L. Pivovarov, "Transition through the separatrix in the dynamics of a satellite with double rotation," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 5, pp. 741-746, 2000.
18.  A. V. Borisov and I. S. Mamaev, Dynamics of Solids [in Russian], RKhD, Moscow-Izhevsk, 2001.
19.  V. S. Aslanov and A. V. Doroshin, "Stabilization of the descent capsule by partial spinning in the realization of an uncontrolled descent in the atmosphere," Kosmicheskie Issledovaniya, Vol. 40, No. 2, pp. 193-200, 2002.
20.  V. S. Aslanov and A. V. Doroshin, "Motion of a system of coaxial bodies of variable mass," PMM [Applied Mathematics and Mechanics], Vol. 68, No. 6, pp. 999-1009, 2004.
21.  N. N. Bukhgolts, Basic Course of Theoretical Mechanics. Part 2 [in Russian], Nauka, Moscow, 1972.
22.  V. V. Golubev, Lectures on Integration of Equations of Motion of Heavy Rigid Bodies near the Fixed Point [in Russian], Gostekhizdat, Moscow, 1953.
23.  V. S. Aslanov, Spatial Motion of Reentering Body [in Russian], Fizmatlit, Moscow, 2004.
24.  H. Goldstein, Classical Mechanics [Russian translation], Nauka, Moscow, 1975.
25.  G. Lamb, Theoretical Mechanics. Volume 3 [in Russian], Glav. Red. Obshchetekhn. Lit-ry, Moscow-Leningrad, 1936.
Received 23 May 2005
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