Nonplanar Periodic Solutions for Spatial Restricted N+1-Body Problems
  We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a non-planar periodic solution for any $N\geq2$. 
Fengying Li and Shiqing Zhang and Xiaoxiao Zhao
math-ph math.MP