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

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. A semi-analytical method of constructing the series solution up to an arbitrary order for relative motion near equilibrium systems is proposed facilitate design formations based on a Lindstedt–Poincaré method. The details expansion and coefficient $$m\!:\!n$$ -period orbits are discussed. To verify effectiveness method, practical convergence domain high-order computed by comparing it with corresponding numerical solutions that satisfy specified boundary conditions. Simulation results demonstrate efficacy systems.