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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 unduloid ： ウィキペディア英語版 unduloid In geometry, an unduloid, or onduloid, is a surface with constant nonzero mean curvature obtained as a surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve around the line. Image:Unduloid.jpg|This is a computer-generated unduloid created using Maple 12. == Formula == Let $\backslash operatorname(u,k)$ represent the normal Jacobi sine function and $\backslash operatorname(u,k)$ be the normal Jacobi elliptic function and let $\backslash operatorname(z,k)$ represent the normal elliptic integral of the first kind and $\backslash operatorname(z,k)$ represent the normal elliptic integral of the second kind. Let ''a'' be the length of the ellipse's major axis, and ''e'' be the eccentricity of the ellipse. Let ''k'' be a fixed value between 0 and 1 called the modulus. Given these variables, : $\backslash operatorname(u)\; =\; -a(1-e)(\; \backslash operatorname(\backslash operatorname(u,k),k)\; +\; \backslash operatorname(1,k))\; -\; a(1+e)(\; \backslash operatorname(\; \backslash operatorname(u,k),k)\; +\; \backslash operatorname(1,k))\; \backslash ,$ : $\backslash operatorname(u)\; =\; a(1+e)\backslash operatorname(u,k)\; \backslash ,$ The formula for the surface of revolution that is the unduloid is then : $\backslash operatorname(u,v)\; =\; \backslash langle\; \backslash operatorname(u),\; \backslash operatorname(u)\; \backslash cos(v),\; \backslash operatorname(u)\; \backslash sin(v)\backslash rangle\; \backslash ,$ 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「unduloid」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.