Coulomb spacecraft formation flying: Equilibrium points, periodic orbits, and center manifolds

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. To achieve a deeper understanding of the dynamical structures of Coulomb formations, in this paper, an eight-charge symmetric configuration of Coulomb formation is presented and its dynamics is analyzed by center manifold reduction and Poincaré maps. The Hamiltonian equations of motion for the Coulomb formation are derived on the basis of Clohessy–Wiltshire equations. Equilibrium configurations of the Coulomb formation and their corresponding linearized vector fields in different charging scenarios are studied. Nonlinear dynamics near the equilibrium points is investigated with center manifold reduction based on Lie series method. Poincaré maps are employed to describe the bounded motions of the reduced Hamiltonian system. Numerical results indicate that there exist two families of Lyapunov periodic orbits, 1:1 and 1:2 resonance halo orbits, chaotic orbits, and two-dimensional invariant tori and the center manifold is capable of capturing all the dynamics in different charging scenarios.