Application of classical differential geometry theory to the study of missile guidance problem.

摘要

In this thesis, an innovative approach is followed for the study of missile guidance problem. The moving orthogonal coordinate system studied in classical differential geometry curve theory is similar to the stability axis system studied in atmospheric flight mechanics. The spatial rate of variation of a moving coordinate system (the Frenet-Serret formula) corresponds to the motion of a stability axis system. Based on this similarity, the Frenet-Serret formula together with the characteristics of a fictitious missile pointing device are used to design a new missile guidance curvature command.; In two dimensional missile guidance problem, based on the capture and miss characteristics, two different qualitative analysis approaches are introduced to study the capture capability of the designed guidance curvature command. First, by comparing the rotations of the velocity vectors of missile and target which follows straight and circular flight paths, sufficient initial conditions for capture are studied by following the sequences of engagement. Second, the characteristics of missile missing vectors are used to find a more conservative sufficient initial condition which, based on target's maneuvering information, can guarantee capture under arbitrary target maneuver.; In three dimensional engagements, the missile curvature command is derived based on the same arguments as in two dimensional engagements. The second method applied in two dimensional engagements can be extended to three dimensional engagements directly. In this case, two missile torsion commands are introduced together with modified sufficient initial launch envelopes which, based on target's maneuvering information, can guarantee capture for arbitrary target maneuver.; Since capture and miss exist in different regions of the parametric space between rate of rotation of the line of sight vector and distance between missile and target, it is concluded that if the responses of these two parameters avoid the region in which miss can occur, then miss simply will not occur, no matter what are the missile command, missile and seeker dynamics, or the target's maneuver.