Generating families in the restricted three-body problem
By: Michel Hénon.
Series: Lecture notes in physics.; m52, m65
Publisher: Springer-Verlag; Springer
Published: 1997
Place of publication: Berlin; New York
Language: eng
Number of pages: 278
Subjects: Three-body problem.; Celestial mechanics.; Artificial satellites -- Orbits.; Bifurcation theory.
Description: 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.
Notes: Includes bibliographical references and indexes.
Table of contents: title: [I. No special title]; title: II. Quantitative study of bifurcations.