Astrophysics and Space Science

, Volume 183, Issue 2, pp 199–213 | Cite as

Periodic solutions and their stability for the problem of gyrostat

  • F. M. El-Sabaa
Article

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.

Keywords

Periodic Solution Hamiltonian Function 

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References

  1. Arkanjeleski, Y.: 1977,Lectures on the Dynamics of a Rigid Body, Moscow.Google Scholar
  2. Deprit, A.: 1967,Amer. J. Phys. 53, 1, 424.Google Scholar
  3. Euler, L.: 1785,Découverte d'une nouveau principe de méchanique, Mémoires de l'Acad. des Sci. de Berlin, Vol. 14, pp. 154–193.Google Scholar
  4. Hori, G.: 1966,Publ. Astron. Soc. Japan 18(4), 287.Google Scholar
  5. Lagrange, J.: 1888,Mécanique analytique, Gauthier-Villars, Paris.Google Scholar
  6. Levi-Civitá, T. and Amaldi, U.: 1927,Lezioni di Meccanica Razionale, Vol. II, Bologna.Google Scholar
  7. Markov, A. and Churkina, N.: 1985,Astron. Letters 11(8), 267.Google Scholar
  8. Poincaré, H.: 1892–1899,Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (reprinted by Dover, New York, 1957).Google Scholar
  9. Poincaré, H.: 1905,Leçons de mécanique céleste, Vol. 1, Gauthier-Villars, Paris.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • F. M. El-Sabaa
    • 1
  1. 1.Kuwait UniversityKuwait

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