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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 Beltrami vector field ： ウィキペディア英語版 Beltrami vector field In vector calculus, a Beltrami vector field, named after Eugenio Beltrami, is a vector field in three dimensions that is parallel to its own curl. That is, F is a Beltrami vector field provided that :$\backslash mathbf\backslash times\; (\backslash nabla\backslash times\backslash mathbf)=0.$ If $\backslash mathbf$ is solenoidal - that is, if $\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; 0$ such as for an incompressible fluid or a magnetic field, we may examine $\backslash nabla\; \backslash times\; (\backslash nabla\; \backslash times\; \backslash mathbf)\; \backslash equiv\; -\backslash nabla^2\; \backslash mathbf\; +\; \backslash nabla\; (\backslash nabla\; \backslash cdot\; \backslash mathbf)$ and apply this identity twice to find that ::$-\backslash nabla^2\; \backslash mathbf\; =\; \backslash nabla\; \backslash times(\backslash lambda\; \backslash mathbf)$ and if we further assume that $\backslash lambda$ is a constant, we arrive at the simple form :$\backslash nabla^2\; \backslash mathbf\; =\; -\backslash lambda^2\; \backslash mathbf.$ Beltrami vector fields with nonzero curl correspond to Euclidean contact forms in three dimensions. The vector field :$\backslash mathbf\; =\; -\backslash frac\; +\; \backslash frac$ is a multiple of the standard contact structure −''z'' i + j, and furnishes an example of a Beltrami vector field. ==See also== *Complex lamellar vector field *Conservative vector field 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「Beltrami vector field」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.