Rotation–translation coupling analysis on perturbed spacecraft relative translational motion

This paper explores an accurate and complete spacecraft six-degree-of-freedom coupled relative motion model using the dual quaternion representation. Based on this technique, we build a scheme capable of describing both kinematic and dynamic coupling effects on the spacecraft relative translational motion through a further combination with the chaser’s precise absolute translational and rotational dynamics. This new model generalizes the existing nonlinear spacecraft relative translational model to include both the kinematic coupling effect due to the displacements of selected feature points relative to the spacecraft centers of mass and the dynamic coupling effect induced by the gravity gradient torque and the orbital perturbations. Several numerical simulations are implemented to validate the feasibility of the proposed model, for analyzing both the kinematic and dynamic coupling effects, on the relative translational motion of two arbitrary feature points in either Keplerian or J₂ perturbed orbits. The results are further compared against the J₂ perturbation effect.