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Generating Families in the Restricted Three-Body Problem

  • Book
  • © 1997

Overview

Authors:
  1. Michel Hénon

    1. CNRS, Observatoire de la Côte d’Azur, Nice Cedex 4, France

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  • The first classification of the orbit structure of a seemingly non-integrable system in every detail

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    Pages 1-4

  3. Definitions and Properties

    Pages 5-19

  4. Generating Orbits of the First Species

    Pages 21-33

  5. Generating Orbits of the Second Species

    Pages 35-77

  6. Generating Orbits of the Third Species

    Pages 79-94

  7. Bifurcation Orbits

    Pages 95-124

  8. Junctions: Symmetry

    Pages 125-135

  9. Junctions: Broucke’s Principle

    Pages 137-169

  10. Fragments

    Pages 171-202

  11. Generating Families

    Pages 203-233

  12. Back Matter

    Pages 235-278
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Keywords

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.

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

Authors and Affiliations

  • CNRS, Observatoire de la Côte d’Azur, Nice Cedex 4, France

    Michel Hénon

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