• 作者： 孫方鐸
• 作者服務機構： 國立清學大學
• 中文摘要： 本文係對反平方力場中雙點軌道族所作之全域性分析。此雙點中一為定點，另一則為變點，常位置於通過力場中心之直線上，由是此族實屬刻普勒式之平面族，具有一共點及共同之射程角，但其終始兩點之動徑比則為一變數，此族在形相空閒之示相極為複雜，但經過正規化矢速座標轉換後，其映像即變為簡單，使吾人得以根據其幾何性質對此彈道族之全域性質獲得若干認識。例如族內彈道各項參變數變化之限度，兩點間小角航行與大角航行彈道之差異，及各子族之特性等等，包括「等時族」之初步研究在內。在分析過程中曾提出「共輓彈道族」之概念，並應用「反演變換」加以推演，上述之全域性觀察，意在對兩點彈道之分析提供一廣泛之基礎，期能對定時與不定時之彈道飛行問題之解答有所裨益。
• 英文摘要： A global analysis of the family of trajectories through one fixed pointand another variable point in a Newtonian gravity field is presented. Thevariable point is assumed to lie on a fixed line through the field center,Thus the family studied is a planar Keplerian family having one commonterminal point and a common range angle. but. varying distance ratio. Thecomplexity of the family is first simplified by transforming it from theconfiguration space to the velocity space by the normalized hodographicmapping, and the global characteristics of the family is then observed fromits image in the velocity space, From such study the limitations on theprincipal orbital parameters of the family are found, and many interestingproperties of the family and its subfamilies are discovered. Among thesubfamilies considered, some preiliminary investigation on the isochronaltrajectories are presented and the isochronal lines are mapped. To help theanalysis the concept of conjugate trajectory families is introduced, and infinding such a conjugate pair the method of inversion is applied and illustrt-ed. It is hoped that the global view of the trajectory family presentedherein would form a broad basis for the analytical treatment of two-ter-urinal space trajectories under open-or fixed-time conditions.
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