Celestial Mechanics and Dynamical Astronomy

, Volume 90, Issue 1–2, pp 13–33 | Cite as

The global flow of the parabolic restricted three-body problem

  • Josep M. CorsEmail author
  • Jaume Llibre


We have two mass points of equal masses m1=m2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m3=0, the motion of m1 and m2 is not affected by the third and from the symmetry of the motion it is clear that m3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m3. Our main result is the characterization of the global flow of this problem.


global flow restricted three-body problem Sitnikov problem 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada III, Escola Universitària Politècnica de ManresaUniversitat Politècnica de CatalunyaManresa, BarcelonaSpain
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraBarcelonaSpain

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