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IssuesArchive of Issues2003-4pp.21-27

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V. N. Koshlyakov, "On the transition to the precessional equations in non-conservative gyroscopic systems," Mech. Solids. 38 (4), 21-27 (2003)
Year 2003 Volume 38 Number 4 Pages 21-27
Title On the transition to the precessional equations in non-conservative gyroscopic systems
Author(s) V. N. Koshlyakov (Kiev)
Abstract The aim of this paper is to investigate a mechanism of domination of gyroscopic forces in non-conservative systems. The investigation is based on a matrix equation that has been obtained in [1, 2]. A comparison of matrices occurring in this equation in norm enables one to identify a mechanism responsible for domination of gyroscopic forces in systems acted upon by non-conservative forces. The presentation of the material is associated with the problem of transition to precessional equations in non-conservative gyroscopic systems. An illustrative example is considered.
References
1.  V. N. Koshlyakov, "On structural transformations of non-conservative systems," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 6, pp. 933-941, 2000.
2.  V. N. Koshlyakov and V. L. Makarov, "To the theory of gyroscopic systems with non-conservative forces," PMM [Applied Mathematics and Mechanics], Vol. 65, No. 4, pp. 698-704, 2001.
3.  A. Yu. Ishlinskii, "On the equations of the precessional theory of gyroscopes in the form of the equations of motion of the representative point in the picture plane," PMM [Applied Mathematics and Mechanics], Vol. 23, No. 5, pp. 801-809, 1959.
4.  D. R. Merkin, Gyroscopic Systems [in Russian], Nauka, Moscow, 1974.
5.  V. S. Novoselov, "Motion of gyroscopic systems," PMM [Applied Mathematics and Mechanics], Vol. 23, No. 1, pp. 176-178, 1959.
6.  A. I. Kobrin, Yu. G. Martynenko, and I. V. Novozhilov, "On the precessional equations for gyroscopic systems," PMM [Applied Mathematics and Mechanics], Vol. 40, No. 2, pp. 230-237, 1976.
7.  E. Ya. Gorelova and V. V. Strygin, "Complete separation of motions in some systems of gyroscopic type," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 8-13, 1985.
8.  V. V. Strygin and V. A. Sobolev, Separation of Motion by means of Integral Transformations [in Russian], Nauka, Moscow, 1988.
9.  I. I. Metelitsyn, "To the issue of gyroscopic stabilization," Doklady AN SSSR, Vol. 86, No. 1, pp. 31-34, 1952.
10.  B. V. Bulgakov, Applied Theory of Gyroscopes [in Russian], Izd-vo MGU, Moscow, 1976.
11.  V. V. Beletskii, The Motion of an Earth Satellite Relative to the Center of Mass [in Russian], Nauka, Moscow, 1965.
12.  L. D. Akulenko, D. D. Leshchenko, and F. L. Chernousko, "Rapid motion of a heavy rigid body with a fixed point in a resisting medium," Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 5-13, 1982.
13.  F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow, 1967.
14.  N. G. Chetaev, Stability of Motion [in Russian], Nauka, Moscow, 1965.
15.  R. A. Horn and C. R. Johnson, Topics in Matrix Analysis [Russian translation], Mir, Moscow, 1989.
16.  Ya. N. Roitenberg, Gyroscopes [in Russian], Nauka, Moscow, 1975.
17.  S. A. Agafonov, "On the asymptotic stability of non-conservative systems," Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 3-8, 1988.
Received 12 December 2002
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