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Equilibrium Connections on the Triple Collision Manifold

  • A. Susín
  • C. Simó
Part of the NATO ASI Series book series (NSSB, volume 272)

Abstract

In the three body problem the triple collision manifold plays a fundamental role to describe passages near triple collision. To study the possible transitions from the approach to collision to the escape from it, the invariant submanifolds on that manifold are essential. In this paper we study mainly the connections between the equilateral approaches and escapes.

Keywords

Configuration Space Unstable Manifold Solid Torus Central Configuration Triple Collision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Moeckel, R., Chaotic Dynamics Near Triple Collision, Arch. Rat. Mechanics and Analysis 107 (1989), 37–70.MathSciNetADSMATHGoogle Scholar
  2. 2.
    Simó, C., Masses for which Triple Collision is Regularizable, Celestial Mech. 21 (1980), 25–36.MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Simó, C Analysis of triple collision in the isosceles problem, in "Classical Mechanics and Dynamical Systems", Ed. R. L. Devaney and Z. Nitecki, Marcel Dekker, 1981, pp. 203–224.Google Scholar
  4. 4.
    Simó, C.; Susín, A., Connections between critical points in the collision manifold of the planar 3-body problem, To appear Proceed. Workshop on the Geometry of Hamiltonian Systems, Berkeley (1989).Google Scholar
  5. 5.
    Susín, A., Passages Near Triple Collision, in "Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems," Ed. A E Roy. Reidel, 1988, pp. 505–513.Google Scholar
  6. 6.
    Waldvogel, J., Symmetric and regularized coordinates on the plane triple collision manifold, Celestial Mech. 28 (1982), 69–82.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • A. Susín
    • 1
  • C. Simó
    • 2
  1. 1.Dept. de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Dept. de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain

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