Generating Families in the Restricted Three-Body Problem

1. Front Matter

   Pages I-XII

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2. Definitions and General Equations

   Pages 1-16

3. Quantitative Study of Type 1

   Pages 17-38

4. Partial Bifurcation of Type 1

   Pages 39-78

5. Total Bifurcation of Type 1

   Pages 79-91

6. The Newton Approach

   Pages 93-129

7. Proving General Results

   Pages 131-148

8. Quantitative Study of Type 2

   Pages 149-179

9. The Case 1/3 < v < 1/2

   Pages 181-197

10. Partial Transition 2.1

    Pages 199-224

11. Total Transition 2.1

    Pages 225-238

12. Partial Transition 2.2

    Pages 239-269

13. Total Transition 2.2

    Pages 271-281

14. Bifurcations 2T1 and 2P1

    Pages 283-296

15. Back Matter

    Pages 297-301

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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

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

  Michel Hénon

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