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Sur les solutions périodiques du mouvement plan de libration des satellites et des planètes

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Résumé

Ce papier présente une étude analytique du mouvement plan de rotation des satellites (et des planètes) dans leurs mouvements orbitaux. Les trois familles des solution périodiques sont obtenues par la méthode du prolongement analytique de Poincaré. Ensuite, la stabilité de ces solutions périodiques est discutée, et les équations approchées des courbes limites de stabilité sont données jusqu'au quatrième ordre.

Abstract

This paper presents an analytical study of the rotational motion of the satellites (and the planets) in their orbital planes. The three families of periodic solutions are obtained by the method of analytical continuation as formulated by Poincaré. The stability of these solutions are analyzed, and the approximate equations of the transition curves are obtained to the fourth order.

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Références

  • Beletskii, V. V.: 1966, ‘Motion of an Artificial Satellite About Its Center of Mass’, NASA TTF-429.

  • Chernousko, F. F.: 1963,U.S.S.R. Comput. Math. Math. Phys. 3, 699–713.

    Google Scholar 

  • Deprit, A. et Rom, A. R. M.: 1967,Bull. Astron. 2, Fasc. 3, 425–447.

    Google Scholar 

  • Jefferys, W. H.: 1966,Science, No. 151, 1384.

    Google Scholar 

  • Kovalevsky, J.: 1963,Introduction à la Mécanique Céleste, Librairie Armand Colin, Paris.

    Google Scholar 

  • Liu, F. C.: 1971,AIAA J. 9, 1240–1244.

    Google Scholar 

  • Liu, H. S. et O'Keeffe, J. A.: 1965,Science, No. 150, 1717.

    Google Scholar 

  • Lutze, F. H. Jr. et Abbitt, M. W. Jr.: 1969,Celes. Mech. 1, 31–35.

    Google Scholar 

  • Modi, V. J. et Brereton, R. C.: 1969,AIAA J. 7, 1217–1225.

    Google Scholar 

  • Moulton, F. R.: 1920,Periodic Orbits, Cargenie Inst. of Washington, Washington D.C.

    Google Scholar 

  • Pacault, R.: 1969, ‘Synchronisme de la Rotation et du Mouvement Orbital des Planètes (Mercure) et des Satellites’, Note scientifique, ESRO, No. SN-92.

  • Torzhevkii, A. P.: 1964,Kosm. Issled., Tome 2, No. 5, 667–678.

    Google Scholar 

  • Vinh, N. X.: 1970,Celes. Mech. 2, 64–76.

    Google Scholar 

  • Zlatoustov, V. A., Okhotsimskii, D. E., Sarychev, V. A., et Torzhevskii, A. P.: 1964,Kosm. Issled. Tome 2, No. 5, 658–666.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, Univ. of Michigan, Ann Arbor, Mich, USA

    Nguyen X. Vinh

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  1. Nguyen X. Vinh
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Vinh, N.X. Sur les solutions périodiques du mouvement plan de libration des satellites et des planètes. Celestial Mechanics 8, 371–403 (1973). https://doi.org/10.1007/BF01227807

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  • DOI: https://doi.org/10.1007/BF01227807

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