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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 Joukowsky transform ： ウィキペディア英語版 Joukowsky transform In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky, is a conformal map historically used to understand some principles of airfoil design. The transform is : $z=\backslash zeta+\backslash frac$, where $z=x+iy$ is a complex variable in the new space and $\backslash zeta=\backslash chi\; +\; i\; \backslash eta$ is a complex variable in the original space. This transform is also called the Joukowsky transformation, the Joukowski transform, the Zhukovsky transform and other variations. In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the ''z'' plane by applying the Joukowsky transform to a circle in the $\backslash zeta$ plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the point $\backslash zeta$ = −1 (where the derivative is zero) and intersects the point $\backslash zeta$ = 1. This can be achieved for any allowable centre position $\backslash mu\_x\; +\; i\backslash mu\_y$ by varying the radius of the circle. Joukowsky airfoils have a cusp at their trailing edge. A closely related conformal mapping, the Kármán–Trefftz transform, generates the much broader class of Kármán–Trefftz airfoils by controlling the trailing edge angle. When a trailing edge angle of zero is specified, the Kármán–Trefftz transform reduces to the Joukowsky transform. ==General Joukowsky transform== The Joukowsky transform of any complex number $\backslash zeta$ to $z$ is as follows :$$ \begin z &= x + iy =\zeta+\frac \\ &= \chi + i \eta + \frac \\ &= \chi + i \eta + \frac \\ &= \frac + i\frac. \end So the real (''x'') and imaginary (''y'') components are: :$$ \begin x &= \frac \qquad \text \\ y &= \frac. \end 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「Joukowsky transform」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.