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Three-dimensional periodic solutions around equilibrium points in Hill's problem

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Abstract

The three-dimensional periodic solutions originating at the equilibrium points of Hill's limiting case of the Restricted Three Body Problem, are studied. Fourth-order parametric expansions by the Lindstedt-Poincaré method are constructed for them. The two equilibrium points of the problem give rise to two exactly symmetrical families of three-dimensional periodic solutions. The familyHL e2v originating at L2 is continued numerically and is found to extend to infinity. The family originating at L1 behaves in exactly the same way and is not presented. All orbits of the two families are unstable.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Patras, Greece

    C. Zagouras

  2. Dept. of Engineering Science, University of Patras, Greece

    V. V. Markellos

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  1. C. Zagouras
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  2. V. V. Markellos
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Zagouras, C., Markellos, V.V. Three-dimensional periodic solutions around equilibrium points in Hill's problem. Celestial Mechanics 35, 257–267 (1985). https://doi.org/10.1007/BF01227656

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  • DOI: https://doi.org/10.1007/BF01227656

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