The Three-Body Problem

  • Dino Boccaletti
  • Giuseppe Pucacco
Part of the Astronomy and Astrophysics Library book series (AAL)

Abstract

Historically, the three-body problem is the most important problem of celestial mechanics and for about two centuries has also been the most extensively studied problem of the whole mathematical physics. In this chapter, we consider only the “classical” subjects, while the more “modern” ones (KAM theory, chaotic solutions, etc.) find their place in the Volume 2. Of course, we have tried to fashion the treatment of the subject in such a way that it seems quite natural to insert subsequent developments. It is very hard, indeed impossible, in so little room, to succeed in introducing all the main problems; therefore, we have made a choice, consistent with the general intention of the book. For the rest, we have endeavoured to provide the reader with the tools and the information necessary for continuing to study the subject in specialized books or original papers.

Keywords

Manifold Peri Librium Rium Univer 

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Bibliographical Notes

  1. C. Marchal: The three-body problem (Elsevier, 1990).Google Scholar
  2. Y. Hagihara: Celestial Mechanics, Vol. IV (Japan Society for the Promotion of Science, 1975 ).Google Scholar
  3. K. G. J. Jacobi: Sur le mouvement d’un point et sur un cas particulier du problème des trois corps, Compte Rendu de l’Académie des Sciences, Paris, pp. 59–61 (1836).Google Scholar
  4. A. M. Leontovich: On the stability of Lagrange’s periodic solutions of the restricted three-body problem, Soviet Math. Dokl. 3, 425–429, (1962).MATHGoogle Scholar
  5. A. Deprit, A. Deprit Bartholomé: Stability of the triangular Lagrangian points, Astron. J. 72, 173–179 (1967).ADSCrossRefGoogle Scholar
  6. A. Cook: The Motion of the Moon (Adam Hilger, 1988).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Dino Boccaletti
    • 1
  • Giuseppe Pucacco
    • 2
  1. 1.Dipartimento di Matematica “Guido Castelnuovo”Università degli Studi di Roma “La Sapienza”RomaItaly
  2. 2.Dipartimento di FisicaUniversità degli Studi di Roma “Tor Vergata”RomaItaly

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