© 2001

Generating Families in the Restricted Three-Body Problem

II. Quantitative Study of Bifurcations

  • This is an in-depth study of an important model of a non-integrable Hamiltonian dynamical system

  • It will certainly trigger a host of interesting future research


Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 65)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Pages 93-129
  3. Pages 131-148
  4. Pages 181-197
  5. Pages 199-224
  6. Pages 225-238
  7. Pages 239-269
  8. Pages 271-281
  9. Pages 283-296
  10. Back Matter
    Pages 297-301

About this book


The classical restricted three-body problem is of fundamental importance because of its applications in 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 many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.


Approximation Celestial mechanics Dynamical Systems Orbital Dynamics Planetary Science Space Navigation

Authors and affiliations

  1. 1.Observatoire de la Côte d’AzurCNRSNice Cédex 4France

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