同平面間圓軌道之最省燃料轉換軌跡

Minimum-Fuel Trajectories for Transferring between Two Coplanar Circular Orbits

陳育民(Yu-Min Chen) ； 許棟龍(Dong-Long Sheu)

《中國航空太空學會學刊》 36卷2期 (2004/06) Pp. 125-132

https://doi.org/10.6124/TAASRC.200406_36(2).02

摘要

本文以嚴謹之非線性最佳控制理論導出數學模式，並採用二階坡度演算法，配合向後掃掠矩陣方法，以推力方向爲控制變數，求解同平面圓軌道間最省燃料軌道轉換之軌跡。本文以一數值例題驗證所採用之方法，求解及分析最佳轉換軌跡及控制變數之特性；從一已知軌道，利用控制推力方向，達到數個較大高度之軌道。最佳轉換軌道特性顯示，首先會增加速度大小，接著會迅速提升高度，再調整速度之大小以進入目標軌道。另與Hohmann轉換作一比較，顯示此方法燃料需求較大，但是轉換時間縮短許多，連續式推力也比脈衝推力接近實際狀況。

關鍵字

軌道轉換 ； 最佳軌跡 ； 太空力學

並列摘要

The purpose of this study is to investigate the minimum-fuel trajectory for the transfer between coplanar circular orbits with a continuous thrust force of which the direction is adjustable. In this study, a mathematically strict nonlinear optimal control theory is used to formulate the problem. It is then solved by using the second-order gradient method associated with the backward sweep matrix. A numerical example is given to illustrate the methodology. The characteristics of the optimal trajectory and control variable are solved and analyzed. From a given orbit, by varying the direction of a continuous thrust with fixed magnitude, spacecraft is transferred to the orbits with higher altitude. The characteristics of optimal transfer trajectory show that, at first, the magnitude of speed increases, then the altitude rapidly increases, and finally the magnitude of speed is adjusted in order to enter the target orbit. While the orbit transfer with continuous thrust may consume larger amount of fuel as compared with the one with impulsive thrust, the former saves a lot of transferring time, and is more realistic.

並列關鍵字

Orbit transfer ； Optimal trajectories ； Space mechanics