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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 Ellipsoidal coordinates ： ウィキペディア英語版 Ellipsoidal coordinates Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system $(\backslash lambda,\; \backslash mu,\; \backslash nu)$ that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal coordinate system is not produced by rotating or projecting any two-dimensional orthogonal coordinate system. ==Basic formulae== The Cartesian coordinates $(x,\; y,\; z)$ can be produced from the ellipsoidal coordinates $(\; \backslash lambda,\; \backslash mu,\; \backslash nu\; )$ by the equations :$$ x^ = \frac + \mu \right) \left( a^ + \nu \right)} \right) \left( a^ - c^ \right)} :$$ y^ = \frac + \mu \right) \left( b^ + \nu \right)} \right) \left( b^ - c^ \right)} :$$ z^ = \frac + \mu \right) \left( c^ + \nu \right)} \right) \left( c^ - a^ \right)} where the following limits apply to the coordinates :$$ - \lambda < c^ < - \mu < b^ < -\nu < a^. Consequently, surfaces of constant $\backslash lambda$ are ellipsoids :$$ \frac + \lambda} + \frac + \lambda} + \frac + \lambda} = 1, whereas surfaces of constant $\backslash mu$ are hyperboloids of one sheet :$$ \frac + \mu} + \frac + \mu} + \frac + \mu} = 1, because the last term in the lhs is negative, and surfaces of constant $\backslash nu$ are hyperboloids of two sheets :$$ \frac + \nu} + \frac + \nu} + \frac + \nu} = 1 because the last two terms in the lhs are negative. 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「Ellipsoidal 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.