• 作者： 孫方鐸
• 作者服務機構： 國立清華大學應用數學研究所
• 中文摘要： 在聯接中心重力場內兩點之諸橢圓軌道中，於一定之運行週數下，有一最短時問軌道存在，為Lancaster與Blanchard二氏所發現(1969)，但對此之分析研討尚付闕如。本文首就此項軌道之存在，暨其絕對性與唯一性予以數學證明，然後進而分析此最短時問暨其軌道與此兩點對力場中心之位置，及其預定之運行週數間之關係，並尋求其特性，此種最短時間軌道所應滿足之方程式具有高度之超越性(transcendentality)，其一般性之確解幾不可能。為此本文特提供一項圖解法，作為數值解答之一助，兼以此與所用分析方法相印證。由於此項最短時間對朗布特(Lambert)問題之多重解具有決定性之作用，希望本文之分析與所得數值結果對朗氏問題之求解有所裨益。
• 英文摘要： This report presents an analytic study on the minimum time trajectory between two terminal points in space when multi-revolution on elliptic circuits is allowed. Although such minimum flight time has been graphically manifested in the diagrammatic representation of the solutions of Lambert problem in current literature for some time, so far no analytic study on such minimum has been found. In this paper the existence of such a minimum, its nature, and its uniquness are for the first time rigorously proved. With such analytic study as a basis, the variation of the minimum time solution with the geometry of the two-terminal configuration and the prescribed number of complete circuits is investigated; and the characteristic features of the minimum time flight path are explored. To aid the numerical solution of the cumbersome governing equations and to illustrate the analytic findings, a graphical method of solution is also introduced. In view of the important role the minium flight time plays in the determination of the multiple solutions of Lambert problem, it is hoped that the present analysis and the numerical results obtained could be helpful in the solution of Lamber problem when multi-revolution is allowed.
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