Comparison of three equations of motion schemes for a space launcher

Abstract

This paper compares three different sets of translation equations of motion for a space launcher. Two of these schemes, the Cartesian and the polar approaches, are widely used and the third one, the full quaternion approach has just been recently introduced. This paper does not present the mathematical development leading to each of them, but it compares the three schemes in terms of accuracy, robustness and computation time. The three schemes produce the exact same trajectory, but the polar one is the best suited for an onboard guidance algorithm as it is quicker to solve.