本論文應用最佳參數控制理論研究一地對地火箭，在一自轉的理想球形地表上之最短時間飛行軌跡。研究中，假設推力為常數，其方向則為時間的線性函數，可以兩個角度定義之。為簡化分析，設每個控制角各有兩個參數，因此，總共有四個控制參數。本文即應用參數最佳法導出最佳化之必要條件，這些條件與邊界條件構成一組非線性聯立代數方程式。其解法為先猜出一組包含飛行時間的參數，再以Newton-Raphson法反覆迭代，得出一組收斂的參數。在反覆計算的過程中，狀態變數的終端值，均必須以積分系統方程式得之，因此，當參數收斂後，也同時得到一最佳的飛行軌跡。為了解柯氏力(Coriolis force)對於飛行軌跡之影響，本研究以(一)固定發射點，變化發射方向，(二)固定發射方向，但變化發射點緯度的方式，分析各種條件狀況下之飛行軌跡。結果顯示，在北半球的飛行軌跡有向右轉彎的趨勢，而在南半球的飛行軌跡則有向左轉彎之趨勢。又，由於地球自轉的影響，在同樣航程的情況下，以向東發射之飛行時間為最長，向西發射之飛行時間為最短。

　In this thesis,the minimum-time flight trajectories of a surface-to-surface rocket　flying over a rotating spherical earth are studied　by using the optimal control theory. In this study,　it is assumed that the thrust is a constant and its direction, defined by two angels, a linear function of time. To simplify the analysis,it is assumed that there are two parameters for each control angle, i.e., there are totally four control parameters. A parametric optimization method is applied to derive the necessary conditions for optimality, which plus the boundary conditions are in fact a set of nonlinear simultaneous algebraic equations of the four parameters plus the time of flight. To solve the problem, the four parameters and the time of flight are guessed initially. Then the Newton-Raphson method is used to compute the parameters and the time of flight iteratively until finally they converge. In each iteration, the terminal values of state variables are obtained by integrating the system differential equations. Accordingly, when the set of convergent parameters and the time of flight are obtained, an optimal trajectory is also obtained. In order to understand the effects of Coriolis force on flight trajectories, two approaches are conducted in this study. One is to fit the lauch point but variate the launch direction and the other is to fit the launch direction but variate the latitude of the lauch point. It is found that on the north hemisphere, the flight trajectory has a potential to turn right, while on the south hemisphere, the flight trajectory has a potential to turn left. Also, due to the effect of Earth rotation, the flight time to the east is longer than that to the west under the condition of same range.

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