Geometric Approach to Three-Dimensional Missile Guidance Problem

The Frenet–Serret formula in classical differential geometry curve theory and the characteristics of a Ž ctitious missile pointing velocity vector are used to design missile guidance curvature command. Qualitative analysis is conducted to study capture capability of the designed guidance command in three-dimensional engagements. The region that miss can occur is derived in terms of the tangential component of the kinematics equation. Then, sufŽ cient initial condition is derived, which, with target’s maneuvering information, can guarantee capture for arbitrary targetmaneuver. To validatethis capture conclusion,two simplemissile torsion commandsare introduced to rotate direction of themissile curvature commandto ensure that the curvature command formula iswell deŽ ned. Such missile roll strategy may also help to improve capture capability in the Ž nal phase of an engagement.