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The capture region of a general 3D TPN guidance law for missile and target with limited maneuverability

A method is used to analyze the capture area of general 3D true proportional navigation (TPN) guidance laws. With the aid of the orthogonal by not orthonormal modified polar coordinate (MPC), and three modified polar variables (MPVs), the expression of relative dynamics between target and missile becomes simple, and no trigonometric functions are involved, which makes possible the analysis of capture region for both target and missile with limited maneuverability. It can be shown that the determination of the desired capture area requires only the first two of the MPVs no matter whether the maneuverability of missile and target are limited or not. The boundary of the capture region on the two MPVs phase plane can be shown is composed of stable, unstable manifolds and a particular trajectory which will be indicated in the context. For the case of unlimited missile acceleration and measurable target acceleration, the capture region can be found analytically, while for the other cases, the capture region can be obtained graphically.