GEOMETRIC APPROACH TO 3-DIMENSIONAL MISSILE GUIDANCE PROBLEM

The Frenet-Serret formula in classical differential geometry curve the ory and the characteristics of a fictitious missile pointing velocity vector are used to design missile guidance curvature command. Qualitat ive analysis is conducted to study capture capability of the designed guidance command in three-dimensional engagements, The region that mis s can occur is derived in terms of the tangential component of the kin ematics equation, Then, sufficient initial condition is derived, which , with target's maneuvering information, can guarantee capture for arb itrary target maneuver. To validate this capture conclusion, two simpl e missile torsion commands are introduced to rotate direction of the m issile curvature command to ensure that the curvature command formula is well defined. Such missile roll strategy may also help to improve c apture capability in the final phase of an engagement.