A Variational Method for the Propagation of Spacecraft Relative Motion

A new formulation of the spacecraft relative motion for a generic orbit is presented based on the orbital propagation method proposed by Peláez et al. in 2006 [1]. Two models have been developed. In the first model the method is applied to each spacecraft using a time synchronization of the system dynamical states. In the second model we employ a local orbital reference frame with a linearization of gravitational terms, apply the method to the formation center of mass and propagate the relative dynamics with respect to the center of mass reference orbit. The models are compared in terms of computational speed for the case of a bounded triangular formation