The instability of the rhombus-like central configurations in newton 9-body problem

  • Authors:

  • D. Diarova;N. I. Zemtsova

  • Affiliations:

  • Institute of Oil and Gas, Atyrau, Kazakhstan;Computing Center of RAS, Moscow

  • Venue:
  • CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
  • Year:
  • 2006

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Abstract

E.A.Grebenikov and A.N.Prokopenya proved that rhombus-like central configuration in Newton 5-body problem is unstable. In this article, the problem of existence and stability of the rhombus-like central configurations in Newton 9-body problem, which consists of two homothetic rhombuses, is studied. It is proved that these central configurations are unstable. All computations are executed by means of computer algebra system Mathematica.