Avoiding collisions under topological constraints in variational problems coming from celestial mechanics

Abstract

In a singular potential setting, we generalize a method which allows to show that minimizers under topological constraints of the action functional (or of the Maupertuis one) are collision-free. This methods applies to 3-dimensional problems of celestial mechanics exhibiting a particular cylindrical symmetry, as well as to planar problems of N-centre type, where it gives optimal results.