Footprint calculation methods for a reusable launch vehicle

An important element of an adaptive and reconfigurable guidance and control system is the ability to compute the largest area (footprint) on the earth´s surface that is reachable by the autonomous vehicle under the current operating condition. During an abort situation when it suddenly becomes necessary to divert the vehicle from its original landing site, the knowledge of this reachable area can assist in choosing a safe and available landing site. In the paper, a technique based on calculus of variations is applied to find the footprint of an autonomous vehicle subject to operating constraints.