• 作者： 孫方鐸
• 作者服務機構： 清華大學應用數學研究所
• 中文摘要： 本交係對朗布特(Lambert)時間函數之數學研討。此項函數淵源於Wintner氏表朗氏定理之積分式，乃太空力學上解朗氏問題之基礎。作者過去曾以此積分式為起點就朗氏公式之統一表示有所推演，從而對朗氏力學之處理提供一項新的入手方怯（參考文獻4,6）。本文繼承前作，仍自此項積分式出發，賡續誘導出若干對朗氏問題中任何種類之刻卜勒兩點彈道均可適用之通式，然後據以對朗氏時間函數之基本式及其在橢圓軌道多重運行上適用之補充式分析其特性，尤致意於其在特殊情況下所表現之奇異性，並以一系列之曲線圖表示之。利用此等數式及其圖示，吾人並進而對與朗氏問題關聯之若干特殊彈道，如最小運行時間之兩點彈道，等能量或非等能量之等時彈道族等等扼要加以檢討。 此項基礎研究希望能補充本人之前作，導致吾人對朗氏時間函數之較佳了解，從而對現代化太空力學上若干實用問題之解答，如軌道上之會合與瞄準，定時下之軌道轉移等等有所裨益。
• 英文摘要： A mathematical study of the Lambert's time function, originated from Wintner's integral representa-tion of the Lambert theorem is presented．Following the author's previous work on the universal represen-tation of Lambert's formulas [4，6]，additional universal formulas，valid for all classes of two-terminaltrajectories associated with the Lambert problem are developed．The characteristic features of the basicLambert's time function and its augmented version are then analytically studied, and, in particular, thesingular behavior of these functions in various borderline cases are fully explored and graphically displayed.In the light of such formulas and graphs, several particular kinds of two-terminal trajectories, like those ofminimum time of flight, and the isochronous trajectory families, which are isoenergetic or non-isoenergetic,are briefly reviewed. It is hoped that such a basic study would supplement the author's previous findings soas to lead to a better understanding of the time functions, and facilitate the solution of Lambert problemsarising in various fields of astrodynamic applications, like the orbital rendezvous and targeting,the fixed-time orbital transfers, and many others.
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