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Blow up of collapsing binaries in the planar three body problem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1416)

Abstract

For problems with 3 or more bodies the blow up method allows to study the total collision manifold. In this manifold very hard binaries, with two bodies at a very small relative distance, can appear. Nearby motions, in the physical space, go away from the collision manifold with very high energy, travelling hyperbolically to infinity. In this work we analyze the neighborhood of the limit orbit (the collapsing binary) in the case of 3 bodies in the plane. This limit orbit goes from the triple collision manifold to infinity at an infinite speed.

Keywords

  • Periodic Orbit
  • Body Problem
  • Semimajor Axis
  • Binary Collision
  • 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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© 1990 Springer-Verlag

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Martínez, R., Simó, C. (1990). Blow up of collapsing binaries in the planar three body problem. In: Albert, C. (eds) Géométrie Symplectique et Mécanique. Lecture Notes in Mathematics, vol 1416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097476

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  • DOI: https://doi.org/10.1007/BFb0097476

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52191-4

  • Online ISBN: 978-3-540-46920-9

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