Comparative analysis of Cartesian and curvilinear Clohessy-Wiltshire equations

Abstract

In this paper a derivation of Clohessy-Wiltshire equations in curvilinear coordinates is presented. The determination of curvilinear initial conditions from inertial position and velocity vectors is also included. Focus of the paper isa comparative analysis between Cartesian and curvilinear representations of the Clohessy- Wiltshire equations. The analysis addresses both short- term and long-term accuracy of relative motion predictions. It is shown that a curvilinear Clohessy-Wiltshire representation has a superior performance for along-track formations, in particular for larger separations. Both Cartesian and curvilinearrelative motion representations are applied to a specific formation keeping control scenario based on small satellites flying in an along-track formation in a Low Earth Orbit. When the relative motion representations are used for short-time predictions of relative motion, the representation using curvilinear coordinates also leads to a superior performance of control which in turn results in a reduction of propellant use.