Abstract
The constraints imposed on parameters of a force field and of a symmetrical gyrostat in it are determined, at which regular precession of this gyrostat demonstrate Lyapunov stability (or, respectively, instability).
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References
Routh, E.J., An Elementary Treatise on the Dynamics of a System of Rigid Bodies, Cambridge: Macmillan, 1860. Translated under the title Dinamika sistemy tverdykh tel, Moscow: Nauka, 1983.
Tournaire, Mámoire sur la Rotation des Corps Pesant, C. r. Acad. sci. P, 1860, vol. 50, pp. 476–481.
Merkin, D.R., Giroskopicheskie sistemy (Gyroscopic Systems), Moscow: GITTL, 1956.
Rumyantsev, V.V., Ob ustoichivosti statsionarnykh dvizhenii sputnikov (Stability of Steady State Motions of Satellites), vol. 4 of Matematicheskie metody v dinamike kosmicheskikh apparatov (Mathematical Methods in Spacecraft Dynamics), Moscow: Vychislit. tsentr AN SSSR, 1967.
Skimel’, V.N., On the Problems of Motion Stability of a Heavy Solid Body with a Fixed Point, Prikl. Mat. Mekh., 1956, vol. 20, no. 1, pp. 130–132.
Bentsik, E., Su di un tipo di precessoni regolari per un corpo rigido asimmetrico soggetto a forze newtoniane, Rend. Sem. mat. Univ. Padova, 1968–1969, vol. 41, pp. 252–260. Translated into Russian under the title Ob odnom vide regulyarnoi pretsessii nesimmetrichnogo tela v pole sil n’yutonovskogo prityazheniya (One type of Regular Precession of an Asymmetric Body in the Newtonian Field of Forces), Izv. Akad. Nauk SSSR, Mekh., 1970, no. 2, pp. 3–8.
Gylden, H., Unsdersoekning af fall, der rotationsproblemets loesning kan uttryckas medelst reelt periodiska funktioner af tiden, Oefversigt af Kongl. Vetenskaps-Akademiens foerhandlingar, 1893, Org. 50, no. 2, pp. 63–75.
Skimel’, V.N., Stability of Some Motions of Gyrostats, Trudy KAI, 1962, no. 71, pp. 36–41.
Irtegov, V.D., Invariant Manifolds of Steady Motions and their Stability, Novosibirsk, Nauka, 1985.
Galiullin, I.A., Stability of Regular Precession of a Symmetric Body in a Newtonian Force Field, Kosm. Issled., 1995, vol. 33, no. 1, pp. 107–108. [Cosmic Research, pp. 98–99].
Gray, A., A Treatise on Gyrostatics and Rotational Motion. Theory and Applications, London: Macmillan and Co, 1918.
Gorr, G.V., Kudryashova, L.V., and Stepanova, L.A., Klassicheskie zadachi dinamiki tverdogo tela (Classical Problems of Solid Body Dynamics), Kiev: Naukova Dumka, 1978.
Dzhioeva, M.I., Description of Regular Precessions of a Gyrostat in Potential Force Field, Izv. Ross. Akad. Nauk: Mekh. Tverd. Tela, 2006, no. 5, pp. 11–18.
Smeil, S., Topology and Mechanics, Uspekhi Mat. Nauk, 1972, vol. 27, no. 2 (164)m pp. 77–133.
Godbillion, C., Géométrie Différentielle et Méchanique Analytique, Paris: Herrmann, 1969. Translated under the title Differentsial’naya geometriya i analiticheskaya mekhanika (Differential Geometry and Analytical Mechanics), Moscow: Mir, 1973.
Abraham, R. and Marsden, J.E., Foundations of Mechanics, Reading, Mass.: Addison-Wesley, 1978.
Trofimov, V.V. and Fomenko, A.T., Algebra i geometriya integriruemykh gamil’tonovykh differentsial’nykh uravnenii (Algebra and Geometry of Integrable Hamiltonian Differential Equations), Moscow: Faktorial, 1995.
Kharlamov, P.V., On Equations of Motion for a System of Solid Bodies, in Mekhanika tverdogo tela (Mechanics of Solid Bodies), Kiev: Naukova Dumka, 1972, issue 4, pp. 92–98.
Merkin, D.R., Vvedenie v teoriyu ustoichivosti dvizheniya (Introduction to Theory of Motion Stability), Moscow: Nauka, 1987.
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Original Russian Text © I.A. Galiullin, 2011, published in Kosmicheskie Issledovaniya, 2011, Vol. 49, No. 2, pp. 182–184.
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Galiullin, I.A. Solution to the problem of stability of regular precessions of a symmetrical gyrostat in Newtonian field. Cosmic Res 49, 175–178 (2011). https://doi.org/10.1134/S001095251102002X
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DOI: https://doi.org/10.1134/S001095251102002X