Generating Families in the Restricted Three-Body Problem

  • Michel Hénon

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 52)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Pages 1-4
  3. Pages 95-124
  4. Pages 125-135
  5. Pages 171-202
  6. Pages 203-233
  7. Back Matter
    Pages 235-278

About this book


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.


astronomy bifurcation dynamical systems three-body problem

Authors and affiliations

  • Michel Hénon
    • 1
  1. 1.CNRS, Observatoire de la Côte d’AzurNice Cedex 4France

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63802-5
  • Online ISBN 978-3-540-69650-6
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site