本論文之目的在於分析三節火箭自地球表面至軌道之最省燃料軌跡，以瞭解火箭至軌道之最大酬載。本文以未定參數法，將非線性最佳控制問題，轉化成一組非線性代數聯立方程式，再以Newton-Raphson Method解此組聯立方程式，以得到參數值，進而得控制變數、軌跡特性與最大酬載。研究論文中係假設燃料消耗率為常數，推力維持為各節火箭初始重量的四倍，在此基礎下，研究比衝、推重比與各節燃燒時間對於最大酬載的影響。在給定初始重量及比衝值的情況下，經廣泛的參數研究，本論文獲得火箭最佳分節時間點及每節之最佳推重比。

　　The objective of this thesis is to analyze the minimum-fuel trajectory of a three-stage rocket from the earth surface to a designated orbit in order to determine the maximum payload which the rocket can carry.The nonlinear optimal control problem is solved by using an approximate parametric optimization method.As a result, the original optimal control problem is converted to a set of simultaneous nonlinear algebraic equations with a set of unknown parameters. Newton-Raphson method is then used to solve the set of simultaneous equations to determine the unknow parameters. Accordingly, the optimal control, and then the optimal trajectory and the maximum payload are determined.In this thesis, the fuel consumption rate is assumed to be constant and thrust maintain at four times of the initial weight of rocket in each stage.Based on these assumptions, the effects of the specific impulse, the thrust-to-weight ratio and burning time in each stage on the maximum payload are studied.Given a set of weight and specific impulse, in this thesis, the optimal time of burning and the thrust-to-weight ratio for each stage of rocket are obtained upon vast parametric studies.

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