Nonlinear relative dynamics of Lorentz spacecraft about J 2 -perturbed orbit

The Lorentz force acted on a charged spacecraft via interaction with planetary magnetic field provides new means of propellantless electromagnetic propulsion. Active modulation of the surface charge allows the spacecraft to perform orbital maneuvers. By assuming the Earth’s magnetic field could be modeled as a tilted dipole that co-rotates with Earth, a nonlinear dynamical model describing the orbital motion of Lorentz spacecraft with respect to J₂-perturbed orbit is developed using Lagrangian mechanics. Two potential applications of the proposed model, J₂-perturbed Lorentz-augmented spacecraft hovering and Lorentz-propelled rendezvous, are considered in this paper. Fuel-optimal control strategies are designed for hovering, and optimal trajectory of the specific charge of Lorentz spacecraft for propellantless rendezvous that minimizes the consumption of control energy is also derived via Gauss pseudospectral method. To capture the interactive effect of J₂ perturbations and Lorentz force on relative motion, comparisons are made between results derived from J₂-perturbed model and unperturbed model for both applications. Numerical simulations prove the validity of the proposed relative dynamical model and the applicability of Lorentz force in J₂-perturbed spacecraft hovering and rendezvous. Comparisons show that J₂ perturbation should be considered when long-term hovering is necessary or more precise rendezvous trajectory is required, especially for low Earth orbit where J₂ perturbation is one of the most dominant perturbative forces.