並列タイトル等Optimal Low-Thrust Earth Escape Spiral Trajectories From Geosynchronous Orbit
タイトル（掲載誌）航空宇宙技術研究所報告 = Technical Report of National Aerospace Laboratory TR-704
一般注記A numerical analysis has been carried out on minimum-time low-thrust Earth escape spiral trajectories from geosynchronous orbit. The two-point boundary-value problem has been solved with very good convergence by one of the direct methods(two-dimensional search conjugate gradient method with penalty function), using the digital computer FACOM 203-75. Starting from geosynchronous orbit, the spacecraft increases both its orbital altitude and its total energy E(kinetic energy plus potential energy in Earth’s gravitational field), rotating round the Earth along the spiral trajectory, and then attains the parabolic velocity(E=0). The thrust vector oscillates around the velocity vector, i.e., the tangential direction with the period almost equal to the rotational period of the orbit. It can be pointed out that the synchronization is clearer in the first portion of the trajectory and for a smaller initial acceleration a0. The amplitude of the oscillation increases gradually in the first portion, but begins to decrease in the final portion of the trajectory, and reaches zero at the escape point. Thus, the steering angle β vanishes at final time. This means that the direction of the thrust vector coincides with the direction of the velocity vector. At the same time, the time derivative dβ/dt also vanishes. These two equations, i.e., β=0 and dβ/dt=0, are also derived analytically through optimality condition and transversality conditions. The intial value of β seems to vary from plus to minus at random, not uniformly according to the increase of a0. Therfore, it can not be predicted for any specified a0 whether β will start its history from inside or outside the trajectory. On the other hand, all cases computed show that the thrust vector approaches the tangential direction from inside the trajectory.
資料番号: NALTR0704000
レポート番号: NAL TR-704
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
提供元機関・データベース宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ