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    Title: 飛彈導引律統一分析法:三度空間之延伸
    Authors: 田豐
    Contributors: 淡江大學航空太空工程學系
    Keywords: 飛彈;捕捉區;導引律;改良式極座標;相位平面;Missile;Capture Area;Guidance Law;Modified Polar Coordinate;Phase Plane
    Date: 2001-05
    Issue Date: 2010-01-11 15:14:32 (UTC+8)
    Publisher: 臺北縣:淡江大學
    Abstract: 自飛彈比例導引律被使用以來,許多研究學者針對各種導引律分別提出其性能分析。1997年楊獻東等提出一統一分析方法,發現文獻中所採用之各種比例導引律在此統一方法下,皆為其特例。然其結果僅限於二維空間。本文使用改良式極座標直接利用向量幾何表示法描述目標物、飛彈間之相對運動,並利用此座標之特性,將原本所用兩個向量,兩個純量一階非線性常微分方程(或八個一階純量常微分方程),減化為三個純量一階非線性常微分方程式。藉由簡單數學運算,吾人可證明文獻中所用各種比例導引律,其產生之目標物及飛彈間之相對運動皆可由此三個微分方程充分描述。而楊氏在二維空間所用之統一分析方法,與所得之結論,對非逃逸目標物,亦可直接被推展到三維空間,然對於一般三維逃逸目標物則不適用。
    Since the proportional navigation guidance laws was first introduced,many of the researcheres have proposed different methodologies toinvestigate the correpsonding performances of all the existingguidance laws. In 1997, Yang and Yang introduced a unified approach,in that paper the authors found that under the proposed framework, allthe existing guidance are indeed a special case of the mentionedgeneral guidance law. But their results restricted to two dimensionalspace. To extend the results to three dimensional space, a modifiedpolar coordinate (MPC) is unitized in this paper. It is shown thatwith the property of the modified polar coordinate, the number ofdifferential equations required to describe the relative dynamics canbe reduced from six to three. In addition, using the relativevelocities as nonlinear transformation variables reveals that all theresults for two dimensional space can be applied directly fornonmaneuvering target. However, for maneuvering target, thetransformation does not provide the benifit as it does in the previouscase. A different nonlinear transformation method is inevitablyrequired to overcome the difficulty, which will be discussed in anupcoming paper.
    Relation: 第三屆海峽兩岸航空太空學術研討會論文集,頁373-380
    Appears in Collections:[航空太空工程學系暨研究所] 會議論文

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