Generating Families in the Restricted Three-Body Problem (Lecture Notes in Physics Monographs)

Henon, Michel

ISBN 10: 3662141566 / ISBN 13: 9783662141564

Editore: Springer (edition Softcover reprint of the original 1st ed. 1997), 2013

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It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting. Softcover reprint of the original 1st ed. 1997.

Codice articolo 3662141566-8-1

Dati bibliografici

• Titolo: Generating Families in the Restricted Three-Body Problem (Lecture Notes in Physics Monographs)
• Editore: Springer (edition Softcover reprint of the original 1st ed. 1997)
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3662141566
• ISBN 13: 9783662141564
• Rilegatura: Paperback
• Condizione: Very Good

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Riassunto

Thework described in this has somewhat erratically,over monograph grown, of than a more interest inthe was firstaroused period thirty My subject years. thebeautiful and inBroucke.'sthesis also by see computations drawings (1963; Broucke where familiesof orbits in the restricted three 1968), periodic body for the Earth Moon ratio = were mass problem investigated (/.I 0.012155). These that natural for the existence ofthe a explanation drawingssuggested observed familiesand for the found the of orbits could be shapes perhaps by to the limit + 0. a recourse y As first it a to as as step, appeared catalog completely possible necessary the orbits obtained in this limit. orbits of the first generaiing Generating hadbeen studied andother authors. Poincar6 specZes by (1892) Surprisingly, the two other had been Orbits ofthe however, species apparently neglected. second orbits with or consecutive a species, collisions, present comparatively the ofthe simple problem, only two body problem; no using equations yet had been done.An ofthe systematic ever constituent arcs study inventory was inH6non presented (1968). Also little work had been done on farmlies of orbits of the third very to Hill's A numerical species, was corresponding problem. investigation pub lished inR6non (1969).

Dalla quarta di copertina

The classical restricted problem of three bodies is of fundamental importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. In this book an attempt is made to explain and organize this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. The most critical part is the study of bifurcations, where several families come together and it is necessary to determine how individual branches are joined. Many different cases must be distinguished and studied separately. Detailed 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.