Titlebook: Generating Families in the Restricted Three-Body Problem; Michel Hénon Book 1997 Springer-Verlag Berlin Heidelberg 1997 astronomy.bifurcat

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978-3-662-14156-4Springer-Verlag Berlin Heidelberg 1997

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Generating Orbits of the First Species,plete classification has been achieved only recently with the work of Bruno (1976; 1980a; 1994, Chap. VII) on asymmetric orbits. A review of the results up to 1975 can be found in Hagihara (1975, pp. 264 to 339).

Sigmoidoscopy

Generating Orbits of the Second Species,t is periodic, it has an infinity of collisions. (Note that there can be more than one collision per period.) The collisions separate the orbit into pieces, which we call .. Two consecutive arcs join at a collision; their tangents at the collision form an angle, generally different from zero. This a

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Generating Orbits of the Third Species,es to a point. The period . can probably take any positive value (see below). Thus, generating orbits of the third species can be formally considered as forming a single one-parameter family, which we call the . This family is of a peculiar kind: all orbits are identical in shape since they reduce t

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0940-7677 recipes are given. Their use is illustrated by determining a number of generating families, associated with natural families of the restricted problem, and comparing them with numerical computations in the Earth-Moon and Sun-Jupiter case.978-3-662-14156-4978-3-540-69650-6Series ISSN 0940-7677