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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 Elliptic cylindrical coordinates ： ウィキペディア英語版 Elliptic cylindrical coordinates Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the perpendicular $z$-direction. Hence, the coordinate surfaces are prisms of confocal ellipses and hyperbolae. The two foci $F\_$ and $F\_$ are generally taken to be fixed at $-a$ and $+a$, respectively, on the $x$-axis of the Cartesian coordinate system. ==Basic definition== The most common definition of elliptic cylindrical coordinates $(\backslash mu,\; \backslash nu,\; z)$ is :$$ x = a \ \cosh \mu \ \cos \nu :$$ y = a \ \sinh \mu \ \sin \nu :$$ z = z \! where $\backslash mu$ is a nonnegative real number and $\backslash nu\; \backslash in\; [0,\; 2\backslash pi)$. These definitions correspond to ellipses and hyperbolae. The trigonometric identity :$$ \frac \cosh^ \mu} + \frac \sinh^ \mu} = \cos^ \nu + \sin^ \nu = 1 shows that curves of constant $\backslash mu$ form ellipses, whereas the hyperbolic trigonometric identity :$$ \frac \cos^ \nu} - \frac \sin^ \nu} = \cosh^ \mu - \sinh^ \mu = 1 shows that curves of constant $\backslash nu$ form hyperbolae. 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「Elliptic cylindrical coordinates」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.