Geometric analysis of flight control command for tactical missile guidance

In this paper, unlike other developments in missile guidance which rely on solving a system of coupled nonlinear differential equations, an innovative approach is presented for studying tactical missile guidance. The moving orthogonal coordinate system of classical geometric curve theory is similar to the stability axis system used in atmospheric flight mechanics. Based on this similarity, the Frenet-Serret formula of classical geometric curve theory together with the concept of a pseudo-missile pointing velocity vector are used to analyze and design a missile guidance law. The capture capability of this guidance law is qualitatively studied by comparing the rotations of the velocity vectors of missile and target relative to the line of sight vector. Sufficient initial conditions for capture are found by following sequences of engagement geometry with different initial conditions.