The purpose of this paper is to investigate the G-constrained approximate chattering arc for the minimum-time aerobraking maneuver of the shuttle-type space vehicle at constant altitude. Theoretically, in a chattering arc of the first kind, the control chatters between its maximum and minimum values at an infinite rate. As an example, for flight at constant altitude, the bank angle switches between its positive and negative maximum values at an infinite rate to generate maximum drag. The resulting flight path is along the arc of a large circle and is one-dimensional. There is a complete analytical solution for this theoretical chattering arc. For practical application, switching of the bank control at an infinite rate is not possible. In the approximate chattering arc, the bank control switches at a finite rate. The resulting flight path is two-dimensional and there is the penalty of a shorter longitudinal range. If we allow the vehicle to coast for a short distance and then change to an approximate chattering arc, the longitudinal range is satisfied and longer flight time becomes the penalty. The penalty of longer flight time is minimized by increasing the number of control switchings and, at the same time, selecting the optimal instants for the switchings. It is found that when the number of control switchings is five, the resulting optimal trajectory is good enough. With more times of control switchings, too much numerical computation must be made while the improvement in the performance index is small. The G constraint has a significant effect on the trajectory.
