Periodic Solutions for Circular Restricted N + 1 -Body Problems

Abstract

For circular restricted $N+1$-body problems, we study the motion of a sufficiently small mass point (called the zero mass point) in the plane of $N$ equal masses located at the vertices of a regular polygon. By using variational minimizing methods, for some $N$, we prove the existence of the noncollision periodic solution for the zero mass point with some fixed wingding number.