New stacked central configurations for the planar 5-body problem

Jaume Llibre (1) , Luis Fernando Mello (2) , Ernesto Perez-Chavela (3)

1 UAB - Departament de Matemàtiques [Barcelona]
2 Instituto de Ciências Exatas [Itajuba]
3 Departamento de Matemáticas

A stacked central configuration in the -body problem is one that has a proper subset of the -bodies forming a central configuration. In this paper we study the case where three bodies with masses , , (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses , are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by {1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem.

Mots clés: Planar central configurations; -body problem; Stacked central configurations; 5-body problem

Jaume Llibre, Luis Fernando Mello, Ernesto Perez-Chavela. New stacked central configurations for the planar 5-body problem. Celestial Mechanics and Dynamical Astronomy, 2011, 110 (1), pp.43-52. ⟨10.1007/s10569-011-9342-6⟩. ⟨hal-00630415⟩