<h2>AAS 95-328</h2><h2>Time Parameterization of Oval and Lemniscate Surface Trajectories</h2><h4>R. G. Gist, The Aerospace Corporation, El Segundo, CA</h4><h2> Abstract </h2>The movement of aircraft or ships following a "loitering path," or a repeating pattern about a patrol region, may be modeled by relating the position along the path to the time of travel.  This paper will develop a method of relating time to position along any spatial curve that may be described parametrically.  The position and velocity along this trajectory will be derived.  This method will then be applied to both oval and "figure-8" trajectories at constant altitude at or near the surface of the Earth.<br><br>