Relative motion around artificial lagrange points

This work investigates relative motion around the artificial Lagrange points. Two control strategies are used to analyze the stability of relative motion around artificial Lagrange points. The relative motion is strictly unstable and further investigation shows that it diverges very slowly in the vicinity of some artificial Lagrange points. A parameter is defined to quantify instability of the relative motion. Then, the pseudo-stable regions of artificial Lagrange points are given when different values of the parameter are treated as the critical value of pseudo-stability. A large pseudo-stable region exists for one of two control strategies-the passive control strategy. This paper discusses the passive stability design of a sail, and both the attitude and orbital dynamics are considered simultaneously. An artificial Lagrange point in the pseudo-stable region is used to validate the design method. The results show that both the attitude and relative motion are pseudo-stable.