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.