Periodic Solutions in the Generalized Sitnikov $(N+1)$-Body Problem

Abstract

This paper studies a special restricted $(N+1)$-body problem which can be reduced to the Sitnikov problem with an appropriate positive parameter. According to the number of bodies we prove the existence (or nonexistence) of a finite (or infinite) number of symmetric families of periodic solutions. These solutions bifurcate from the equilibrium at the center of mass of the system.