Formation flying linear modelling

Abstract

An extension of the Hill-Clohessey-Wiltshire equations is presented. The equations refer to the relative motion of two satellites as seen by a Chief undergoing a circular Keplerian motion. Both the Earth oblateness and the air drag are included. The new set of equations is then used to study a simple 100m Leader-Follower formation in a near polar orbit at 600Km of altitude. As the system shows to be linear with time periodic coefficients, Floquet theory is used to determine the stability of the formation and the relative trajectory. Poincar exponents are also determined and discussed.