An Elegant State Transition Matrix

Abstract

The analytic Keplerian 6 × 6 Earth Centered Inertial state transition matrix developed by Goodyear, Battin, and other mathematicians is well known. The primary objectives of this paper are to present a relatively simple formulation of the Keplerian state transition matrix, and to show that the higher-order secular terms associated with the state transition matrices of Goodyear and Battin can be eliminated. Analytic and numerical results indicate that the concern about these unbounded secular terms for numerical integration is not warranted. Comparison of Keplerian, Vinti, and numerical state transition matrices in the Hill-Clohessy-Wiltshire coordinate system (local-vertical coordinate system) further supports this contention since the two secular elements of the Keplerian state transition matrix match closely with those of the Vinti and numerical state transition matrices.