Opuscula Math. 30, no. 4 (), 495-506
http://dx.doi.org/10.7494/OpMath.2010.30.4.495
Opuscula Mathematica

# On the relative equilibrium configurations in the planar five-body problem

Abstract. The number of central configurations in the Grebenicov-Elmabsout model of the planar five-body problem is estimated. An appropriate rational parameterization is used to reduce the equations defining such configurations to some polynomial ones. For the restricted five-body problem a sharp estimation is given by using the Sturm separation theorem.
Keywords: planar five-body problem, relative equilibrium, central configuration, Grebenicov-Elmabsout model.
Mathematics Subject Classification: 70F10, 70F15, 83C10.