High-order analytical solutions of bounded relative motions for Coulomb formation flying

Abstract Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. An analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equi-librium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt-Poincaré method. The details of the series expansion and coefficient solution for Lissajous orbits and arbitrary m : n-period orbits are discussed. To verify the effectiveness of the Lindstedt-Poincaré method in constructing series solutions, the practical convergence domain of series solutions for various bounded orbits is computed by com-parison with the corresponding exact numerical solutions. Given the accuracy requirements of practical formation missions, the configuration design for the Coulomb formation can be carried out conveniently and quickly by employing the proposed series solutions.