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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Centered trochoid ： ウィキペディア英語版 Centered trochoid In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle. Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. Specifically, a centered trochoid is a curve that can be parameterized in the complex plane by : $z\; =\; r\_1\; e^\; +\; r\_2\; e^,\backslash ,$ or in the Cartesian plane by : $x\; =\; r\_1\; \backslash cos(\backslash omega\_1\; t)\; +\; r\_2\; \backslash cos(\backslash omega\_2\; t),$ :$y\; =\; r\_1\; \backslash sin(\backslash omega\_1\; t)\; +\; r\_2\; \backslash sin(\backslash omega\_2\; t),\backslash ,$ where : $r\_1,\; r\_2,\; \backslash omega\_1,\; \backslash omega\_2\; \backslash ne\; 0,\; \backslash quad\; \backslash omega\_1\; \backslash ne\; \backslash omega\_2.\backslash ,$ If $\backslash omega\_1/\backslash omega\_2$ is rational then the curve is closed and algebraic. Otherwise the curve winds around the origin an infinite number of times, and is dense in the annulus with outer radius $|r\_1|\; +\; |r\_2|$ and inner radius $||r\_1|\; -\; |r\_2||$. ==Terminology== Most authors use ''epitrochoid'' to mean a roulette of a circle rolling around the outside of another circle, ''hypotrochoid'' to mean a roulette of a circle rolling around the inside of another circle, and ''trochoid'' to mean a roulette of a circle rolling along a line. However, some authors (for example () following F. Morley) use "trochoid" to mean a roulette of a circle rolling along another circle, though this is inconsistent with the more common terminology. The term ''Centered trochoid'' as adopted by () combines ''epitrochoid'' and ''hypotrochoid'' into a single concept to streamline mathematical exposition and remains consistent with the existing standard. The term ''Trochoidal curve'' describes epitrochoids, hypotrochoids, and trochoids (see ()). A trochoidal curve can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle or in a straight line (but not both moving in a line). In the parametric equations given above, the curve is an epitrochoid if $\backslash omega\_1$ and $\backslash omega\_2$ have the same sign, and a hypotrochoid if they have opposite signs. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Centered trochoid」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.