The state transition matrix for relative motion of formation flying satellites

To minimize fuel consumption, a precise analytic solution for the long term relative motion of formation flying satellites is needed. Such a solution was developed in a previous paper. The solution was based on a geometric transformation and a state transition matrix for relative orbital elements and resulted in a state transition matrix for both osculating and mean elements. The solution used non-singular variables for the eccentricity, true anomaly and argument of perigee to avoid the singularities that develop as the eccentricity approaches zero. In this paper, the previous solution is extended using equinoctial variables to remove the singularities that occur with zero inclination.

The state transition matrix for relative motion of formation flying satellites Conference Paper