See the pdf file attached.
A novel semianalytical technique is proposed for the libration point formation design. It is based on the use of Lindstedt-Poincare (LP) series that approximate the center manifold in the vicinity of the libration point. Any performance factor can be constructed by symbolically manipulating the LP series. For a number of typical formation-keeping objectives, the optimal design parameters are first obtained analytically in a low-order approximation (n=1,2) and then exploited as an initial guess in the numerical optimization procedure for the 15th-order approximation model. The proposed technique is robust, constructive, and versatile: while avoiding the necessity of numerical integration in the highly unstable dynamical environment, we effectively use the full hierarchy of center manifold approximations. The numerical optimization for the high-order approximation model is still low-dimensional and alleviated by a good initial guess obtained from low-order approximation models.