Abstract: Libration points are the five equilibrium solutions in the circular restricted three-body problem (CRTBP).The linearized motions around triangular libration points are typical center×center type.Studies about probes moving around orbits in the vicinity of the libration points have theoretical significance.From the vibrational point of view, the polynomial series are used to derive approximately the relations in different directions during periodic motions, which provides a new point of view to exploring the dynamics and analyzing the overall characteristics of the whole system with general rules.The nonlinear relations in polynomial form between the directions of the planar motions can be treated as constraints to obtain the solutions by numerical integration.Numerical simulations verify the efficiency of the proposed method.The methodology of deriving topological relations has the potential to be extended to circular/elliptical R3BP in three dimensional cases.