Action-Minimizing Orbits in the Parallelogram Four-Body Problem with Equal Masses

摘要

In this paper we prove the existence of a new periodic solution for the planar Newtonian four-body problem with equal masses. On this orbit two mass points travel on one star-shaped closed curve while the other two travel on another and have the opposite orientation. The configuration of the masses changes from square to collinear periodically and remains a parallelogram for all time.