火星大气进入段纵向可达区生成的解析同伦法

To analyze the flight capability of a Mars atmospheric entry vehicle, a method based on the analytical homotopic approach is proposed to generate the reachable longitudinal area (the profile of deployment altitude versus downrange). Three initial auxiliary optimization problems with definitely known solutions are established for the maximum/minimum downrange and maximum/minimum deployment altitude problems respectively. Starting from the auxiliary problems, the original problems of interest can be finally solved by the homotopic method. Based on the solutions of the four optimization problems, the reachable longitudinal area can be determined iteratively by setting a proper continuation parameter. The proposed method is finally tested in the MATLAB environment. The simulation results demonstrate the effectiveness of the method in obtaining the values of the initial costate variables. By selecting the reasonable continuation parameters, the reachable longitudinal area can be determined quickly under different initial flight path angles.