We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the ...

In this paper we give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an ...

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 ...

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the ...

We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for ...

We analyze the families of central configurations of the spatial 5-body problem with four masses equal to 1 when the fifth mass m varies from 0 to +∞. In particular we continue numerically, taking m as a parameter, the ...

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily ...

In this paper we prove, for all p 2, the existence of central configurations of the pn-body problem where the masses are located at the vertices of p nested regular polyhedra having the same number of vertices n and a ...

In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, ...