本論文旨在應用最佳參數化法，分析一地對地火箭之最遠射程飛行軌跡。研究中假設火箭為一質點，在球形地表上飛行。火箭之推力設為常數，推力與速度方向的夾角用以控制飛行方向。因此，在三度空間上，推力與速度的夾角可以兩個角度定義之。設每個角度都是時間的線性函數，則系統共有四個參數。本文以參數最佳化法導出最佳化之必要條件，這些條件構成一組非線性聯立代數方程式。其解法為猜出一組參數，再以 Newton-Raphson 法反覆迭代以得一組收斂的參數。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。為瞭解科氏力 (Coriolis force) 對於飛行軌跡的影響，本研究分別以固定發射點緯度，改變發射方向，以及固定發射方向，改變發射點緯度的方式，分析各種飛行狀況的軌跡，其結論是，北半球的飛行軌跡有向右轉彎的趨勢，而南半球的轉彎有向左轉彎的趨勢。又因為地球自轉的影響，向東發射的射程較向西發射的射程遠。

　　In this thesis, the maximum reachable domain for a rocket flying over a spherical earth surface is analyzed by using the optimal control theory. The rocket is assumed to be a point mass. The direction of rocket is controlled by the angle between the thrust, which is assumed to be constant, and the velocity. The angle between the thrust and the velocity can be defined by two angles in three-dimensional space. Each angle is assumed to be a linear function of the time and therefore there are totally four control parameters in the system. In this study, the necessary conditions for optimality are derived by using a parametric optimization method. These necessary conditions plus the boundary conditions are found to be a set of nonlinear simultaneous algebraic equations of the control parameters and the final time. The problem is solved by first guessing a set of control parameters and the final time and then using the Newton-Raphson method to refine them iteratively. In each iterative process, the state variables at the final time in the necessary conditions and the boundary conditions are determined by integrating the system equations from the initial to the final time, and therefore, when the parameters and the final time are convergent, the 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 fix the latitude of the launch point but variate the heading direction and the other is to fix the heading direction but variate the latitude of the launch point. It is found that the trajectories on the north hemisphere have a potential to turn right while the trajectories on the south hemisphere have a potential to turn left. Also, due to the rotation of the Earth, the range to the east is larger than that to the west.

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