93-175
Approximate Chattering Arc For Aerobraking Maneuver
Jeng-Shing Chern* and Chung-Chen Lai**
Abstract
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 are 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 in-finite 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. Then the longitudinal range is satisfied and longer flight time (1.11% more) becomes the penalty. Further investigation is devote to the approximate chattering arcs with 3, 4, and 5 times of bank control switchings, respectively. The penalty of longer flight time is mini-
mized by increasing the number of control switchings and selecting the optimal time instants for the switchings.
*Senior Scientist. Chung Shan Institute of Science and Technology, P.O. Box 90008-6-7, Lungtan, Taiwan 32526, Republic of China.
**Assistant Scientist. Chung Shan institute of Science and Technology, P.O. Box 90008-6-7, Lungtan, Taiwan 32526, Republic of China.