Generating Families in the Restricted Three-Body Problem by Michel HenonGenerating Families in the Restricted Three-Body Problem by Michel Henon

Generating Families in the Restricted Three-Body Problem

byMichel Henon

Hardcover | November 27, 1997

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The classical three-body problem is of great 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. Here the author explains and organizes 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. Many cases are distinguished and studied separately and detailed recipies are given. Their use is illustrated by determining generating families, and comparing them with numerical computations for the Earth+Moon and Sun-Jupiter systems.
Title:Generating Families in the Restricted Three-Body ProblemFormat:HardcoverDimensions:291 pagesPublished:November 27, 1997Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540638024

ISBN - 13:9783540638025


Table of Contents

Introduction.- Definition and Properties.- Generating Orbits of the First Species.- Generating Orbits of the Second Species.-Generating Orbits of the Third Species.- Bifurcation Orbits.-Junctions: Symmetry.- Junctions: Broucke's Principle.- Fragments.- Generating Families.- Correspondence Between Old and New Notations.- The Domain D2.- Number of Branches.- Index of Definitions.- Index of Notations.- References.

Editorial Reviews

From the reviews "The book is an excellent overview of the state-of-the-art of the restricted three-body problem." Zentralblatt für Mathematik, 1998