Abstract:

In the trapezoidal 4-body problem four particles are arranged by pairs, symmetrically placed with respect to a vertical axis of symmetry and lying on the vertices of a trapezoid. Symmetric particles with respect to this axis of symmetry have equal masses and their initial velocities are also symmetric with respect to the vertical axis of symmetry. This is a three degrees of freedom problem.

This problem is a very rich one from the dynamical point of view. Present several kinds of singularites and different posibilities to escape.

We shall show some results obtained in a joint work with Mario Medina and Claudio Vidal in this problem and some of its relation to other 4-body configurations.