New state transition matrix for relative motion on an arbitrary elliptical orbit

Abstract

A new state transition matrix is described for the nonlinear problem of relative motion on an arbitrary elliptical orbit. A linearization is performed, leading to a set of linear differential equations with time-dependent coefficients. A new and simpler solution to those equations is represented in a convenient state transition matrix form. This new state transition matrix is valid for arbitrary elliptical orbits of 0 ≤ e < 1. The state propagation using the new state transition matrix shows good agreement with numerical results.