衛星發射軌跡的最佳化

Study of Optimal Satellite Launcher Trajectories

邱竣凱(Chun-Kai Chiu)

指導教授 ： 馬德明

淡江大學/工學院/航空太空工程學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00631

摘要

為了解決衛星發射軌跡的最佳化問題，我首先推導出載具動態方程式，接著以變分法找出最佳化軌跡，並針對該軌跡設計出一符合需求之載具。本文遇到的困難在於使用變分法時需要找出拉格朗日乘子的初始條件，為了找出初始條件我使用shooting method 並配上誤差矩陣加快搜尋速度，在本文中誤差矩陣可在兩個和三個未知數的條件下加快搜尋初始條件的速度。

關鍵字

尋找初始條件 ； 拉格朗日乘子 ； 衛星載具最佳軌跡

並列摘要

This paper investigated the optimal satellite launcher trajectories. We derived the equations of motion for the satellite launcher and solved the optimal problem with the method of Hamiltonian minimization. A launcher suited the requirements was proposed.
The main difficulty of solving optimal problem with Hamiltonian Minimization is that we have to search for initial conditions. By using shooting method and Error Matrix, we can find initial conditions and save computing time. In the case of two or three unknown initial conditions, we successfully use Error Matrix to save computing time.

並列關鍵字

Lagrange multipliers ； Optimal Satellite Launcher Trajectories

參考文獻

[1] N. X. Vinh, Optimal Trajectories in Atmospheric Flight, Elsevier, 1981.

[3] D. E. Kirk, Optimal Control Theory An Introduction, Dover Publications, 2004.

[4] Rao, Engineering Optimization; Theory and Practice, John Wiley& Sons, 2009.

[5] T. Ashish, Advanced Control of Aircraft, Spacecraft and Rockets, JOHN WILEY & SONS,LTD, 2011.

[2] D. A. Vallado, Fundamentals of Astrodynamics and Applications, 2th Ed., Microcosm Press and Springer, 2001.