Nonlinear Modeling of Spacecraft Relative Motion in the Configuration Space

A methodology to obtain arbitrary high-order approximations to the relative motion between spacecraft was developed by utilizing the Cartesian configuration space in conjunction with orbital elements. The time-series parameterization of the relative position vector, constitutes a powerful analysis and modeling tool, which provides insight into the relative dynamics of spacecraft formations. The insight obtained was used to design 'natural' orbits for formation flying. It was stated that second-order solutions are suffucient to approximate orbits with high relative inclinations and eccentricities.