We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.

We show the existence of a family of stacked central configurations in the planar five-body problem with a special property. Three bodies m1, m2 and m3, ordered from left to right, are collinear and form an Euler central ...

We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically ...

We study the planar central configurations of the 1 + n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2 ≤ n ≤ 4. Numerically, ...

We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. ...

The main purpose of the paper is the study of the motion of a massless body attracted, under the Newton's law of gravitation, by two equal masses moving in parabolic orbits all over in the same plane, the planar parabolic ...

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. ...

The existence of a new class of inclined periodic orbits of the collision restricted three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for ...