Geometric analysis of missile guidance command

An innovative approach is followed for analysing flight control command for tactical missile guidance with a variable manoeuvering target. The moving orthogonal coordinate system of classical differential geometry curve theory is similar to the stability axis system utilised in atmospheric flight mechanics. Based on this similarity, the Frenet-Serret formula is used to study the characteristics of a pseudomissile pointing velocity vector and used to design a new control command for tactical missile guidance. The closed-form solution for the rate of rotation of the line of sight vector, characteristic of the pseudomissile pointing velocity vector, together with a miss vector are used to study the capture capability of this control command. The region of miss is derived in terms of the tangential component of the kinematics equation. A sufficient initial condition, which can guarantee capture under arbitrary target manoeuvres with bounding information, is proposed.