Geometric approach to three-dimensional missile guidance problem

The Frenet-Serret formula in classical differential geometry curve theory and the characteristics of a fictitious 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, sufficient initial condition is derived, which, with target's maneuvering information, can guarantee capture for arbitrary target maneuver. To validate this capture conclusion, two simple missile torsion commands are introduced to rotate direction of the missile curvature command to ensure that the curvature command formula is well defined. Such missile roll strategy may also help to improve capture capability in the final phase of an engagement.