Analytical solution of generalized 3D proportional navigation

The main goal of this paper is to establish a systematic analysis on three-dimensional (3D) guidance laws. The concept of generalized three-dimensional proportional navigation is introduced and its analytical solution is derived. The three second-order nonlinear differential equations describing the 3D pursuit-evasion scenario are obtained in terms of the unit angular momentum which is an useful index measuring the departure tendency of the relative motion from a fixed plane. The existing difficulties in solving this set of coupled nonlinear equations are conquered and the solution shows that many past studies on the two-dimensional proportional navigation are merely special cases of the present framework.