Abstract
The Hamiltonian function of the problem of gyrostat is written in terms of Deprit's transform. The periodic solutions, using Lie's transform, are given and the condition for their stability is carried out.
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References
Arkanjeleski, Y.: 1977,Lectures on the Dynamics of a Rigid Body, Moscow.
Deprit, A.: 1967,Amer. J. Phys. 53, 1, 424.
Euler, L.: 1785,Découverte d'une nouveau principe de méchanique, Mémoires de l'Acad. des Sci. de Berlin, Vol. 14, pp. 154–193.
Hori, G.: 1966,Publ. Astron. Soc. Japan 18(4), 287.
Lagrange, J.: 1888,Mécanique analytique, Gauthier-Villars, Paris.
Levi-Civitá, T. and Amaldi, U.: 1927,Lezioni di Meccanica Razionale, Vol. II, Bologna.
Markov, A. and Churkina, N.: 1985,Astron. Letters 11(8), 267.
Poincaré, H.: 1892–1899,Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (reprinted by Dover, New York, 1957).
Poincaré, H.: 1905,Leçons de mécanique céleste, Vol. 1, Gauthier-Villars, Paris.
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El-Sabaa, F.M. Periodic solutions and their stability for the problem of gyrostat. Astrophys Space Sci 183, 199–213 (1991). https://doi.org/10.1007/BF00637719
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DOI: https://doi.org/10.1007/BF00637719