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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 Weingarten equations ： ウィキペディア英語版 Weingarten equations Weingarten equations give expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of this surface. These formulas were established in 1861 by German mathematician Julius Weingarten. ==Statement in classical differential geometry== Let ''S'' be a surface in three-dimensional Euclidean space that is parametrized by position vector r(''u'', ''v'') of the surface. Let ''P'' = ''P''(''u'', ''v'') be a fixed point on this surface. Then :$\backslash bold\_\; =\; \backslash frac\; ,\; \backslash quad\; \backslash bold\_\; =\; \backslash frac$ are two tangent vectors at point ''P''. Let n be the unit normal vector and let (''E'', ''F'', ''G'') and (''L'', ''M'', ''N'') be the coefficients of the first and second fundamental forms of this surface, respectively. The Weingarten equation gives the first derivative of the unit normal vector n at point ''P'' in terms of tangent vectors ru and rv: :$\backslash bold\_u\; =\; \backslash frac\; \backslash bold\_u\; +\; \backslash frac\; \backslash bold\_v$ :$\backslash bold\_v\; =\; \backslash frac\; \backslash bold\_u\; +\; \backslash frac\; \backslash bold\_v$ 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「Weingarten equations」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.