Optimal interception of a maneuvering long-range missile

In a Newtonian central force field, the minimum-fuel interception of a satellite, or a ballistic missile, in elliptic trajectory can be obtained via Lawden's theory of primer vector. To secure interception when the target performs evasive maneuvers, a new control law, with explicit solutions, is implemented. It is shown that by a rotation of coordinate system, the problem of three-dimensional interception is reduced to a planar problem. The general case of planar interception of a long-range ballistic missile is then studied. Examples of interception at a specified time, head-on interception and minimum-fuel interception are presented. In each case, the requirement for the thrust acceleration is expressed explicitly as a function of time.