本論文之主旨在應用參數最佳化法，分析飛機在大氣中飛行之最省燃料飛行軌跡。研究中假設飛機為一質點，以推力及負荷因子為控制，並假設兩者為三區段連續之時間多項式函數。最省燃料問題與最遠航程問題為互補之問題，本論文係以航程為性能指標，並導出在固定燃料的情況下最遠航程之必要條件，進而解出符合這些必要條件及終端條件之參數。為了更進一步闡釋理論，本文以數值演算範例作為說明。由於控制函數包含太多參數，非線性代數解困難度極高。本論文僅完成數個簡化之例題，雖無全面性之瞭解，但可提供未來研究此問題者作為基石。

　　The objective of this thesis is to analyze the minimum-fuel trajectory of an aircraft in the atmospheric flight by using a parametric optimization method. In this thesis, the aircraft is assumed to be a particle and the thrust and the load factor the controls which are assumed to be piecewisely continuous polynomial functions of time. The minimum-fuel problem and the maximum-range problem are mutual complementary.By using the range of flight as the performance index, the necessary conditions for optimality are derived. They and the terminal constraints form a set of nonlinear simultaneous algebraic equations which are used for solving the optimal parameters.In order to validate the theory, a numerical example is investigated. Due to the complication of nonlinear algebraic equations of which the number is too large, only several simplified cases are successfully solved. Although the optimal trajectories for minimum-fuel flight are still not understood globally, the results obtained in this study have already established a cornerstone for further investigation of the problem along this line.

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