  This paper introduces a new difference scheme to the difference equations for
N-body type problems. To find the non-collision periodic solutions and
generalized periodic solutions in multi-radial symmetric constraint for the
N-body type difference equations, the variational approach and the method of
minimizing the Lagrangian action are adopted and the strong force condition is
considered correspondingly, which is an efficient method in studying those with
singular potentials. And the difference equation can also be taken into
consideration of other periodic solutions with symmetric or choreographic
constraint in further studies.
