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• W2071275691 abstract "We study the mechanism of bifurcation of three-dimensional periodic orbits from the plane of motion of the primaries. The branchings of simple and double periodic three-dimensional orbits occur at the plane periodic orbits of indifferent vertical stability. These vertical-critical plane orbits are doubly important. Not only are they necessary in order to specify the vertically stable segments of the families of plane periodic orbits, but they are also the starting points of the families of the simplest possible three-dimensional periodic orbits, namely, the simple and double periodic. We describe here suitable numerical techniques for their accurate determination and for their continuation through the range of the mass parameter μ of the problem. We use these techniques to determine the first few vertical-critical orbits of the basic families of periodic orbits of the problem, namely, families l, m, i, h, a, b and c, for the entire range of μ. The initial conditions of over three hundred vertical-critical orbits are given, classified in twenty-one series. Their horizontal stability is also examined and this leads to predictions of where in the range of μ stable three-dimensional periodic orbits may not branch from these basic families." @default.
• W2071275691 created "2016-06-24" @default.
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• W2071275691 date "1981-01-01" @default.
• W2071275691 modified "2023-09-26" @default.
• W2071275691 title "Bifurcations of Planar to Three-Dimensional Periodic Orbits in the Restricted Three-Body Problem" @default.
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• W2071275691 doi "https://doi.org/10.1007/978-94-009-8534-6_11" @default.
• W2071275691 hasPublicationYear "1981" @default.
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