Families of Asymmetric Periodic Orbits in Hill’s Problem of Three Bodies |
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Authors: | Michel Hénon |
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Affiliation: | 1. Observatoire de la C?te d’Azur, C.N.R.S., B.P. 4229, 06304, Nice Cedex 4, France
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Abstract: | We present five families of periodic solutions of Hill’s problem which are asymmetric with respect to the horizontal ξ axis. In one of these families, the orbits are symmetric with respect to the vertical η axis; in the four others, the orbits are without any symmetry. Each family consists of two branches, which are mirror images of each other with respect to the ξ axis. These two branches are joined at a maximum of Γ, where the family of asymmetric periodic solutions intersects a family of symmetric (with respect to the ξ axis) periodic solutions. Both branches can be continued into second species families for Γ → − ∞. |
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Keywords: | Hill’ s problem numerical integration periodic orbits second species families |
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