Linearized relative motion and proximity control of E-sail-based displaced orbits

This paper discusses the linearized relative motion and control of Electric Solar Wind Sails (E-sails) operating in formation flight around a heliocentric displaced orbit. An E-sail is constituted by thin and centrifugally stretched tethers, and generates a propulsion by momentum interaction with the charged particles from the solar wind. Feasible regions and linear stability of circular displaced non-Keplerian orbits generated by E-sails are investigated using the latest thrust model. The linearized relative motion of E-sails in a formation flight is developed in the chief's orbital frame, and a linear stability analysis of the relative motion is carried out with eigenvalue decomposition. Relative trajectories are classified into three categories, according to whether the relative orbit is stable, fully unstable or locally unstable, the latter corresponding to an instability in the along-track direction. Two control strategies are proposed for stabilization, the first one is an active control aiming to change the topology of the relative motion to eliminate the instability caused by positive real eigenvalues, and the other is a closed-loop feedback control to maintain stability in the along-track direction. Numerical simulations indicate a high accuracy of the linearized relative dynamical model and a good performance of the control strategies.