The purpose of this paper is to develop an approximate chattering arc
for a minimum-time aerobraking maneuver for a shuttle-type space
vehicle. Theoretically, in chattering arc of the first kind, the control
chatters between its maximum and minimum values are at an infinite rate.
As an example, for a flight at a constant altitude, the bank angle
switches between its positive and negative maximum value arc at an
infinite rate to generate maximum drag. The resulting flight path is
along the arc of a great circle and is one-dimensional. We have a
complete analytic solution for this theoretical chattering arc. In
practical application, switching of the bank control at an infinite rate
is not possible. An approximate chattering arc with the bank control
switches only two times is then introduced. The resulting flight path is
two-dimensional and there is a penalty of shorter longitudinal range. We
now allow the vehicle to coast for a short distance and then change to
approximate chattering arc. The the longitudinal range is satisfied and
longer flight time (1.11% more) becomes the penalty. Further
investigation is devoted to the approximate chattering arcs with 3, 4,
and 5 times of bank control switchings, respectively. The penalty of
longer flight time is minimized by increasing the number of control switchings and selecting the optimal time instants for the switchings.
