Central configurations of the five-body problem with equal masses

Abstract

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

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Correspondence to Tsung-Lin Lee.

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Lee, T., Santoprete, M. Central configurations of the five-body problem with equal masses. Celest Mech Dyn Astr 104, 369–381 (2009). https://doi.org/10.1007/s10569-009-9219-0

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Keywords

  • Celestial mechanics
  • n-Body problem
  • Central configurations
  • Polyedral homotopy continuation method