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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 Euler–Tricomi equation ： ウィキペディア英語版 Euler–Tricomi equation In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi. :$$ u_=xu_. \, It is hyperbolic in the half plane ''x'' > 0, parabolic at ''x'' = 0 and elliptic in the half plane ''x'' < 0. Its characteristics are :$x\backslash ,dx^2=dy^2,\; \backslash ,$ which have the integral :$y\backslash pm\backslash fracx^=C,$ where ''C'' is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line ''x'' = 0, the curves lying on the right hand side of the ''y''-axis. ==Particular solutions== Particular solutions to the Euler–Tricomi equations include * $u=Axy\; +\; Bx\; +\; Cy\; +\; D,\; \backslash ,$ * $u=A(3y^2+x^3)+B(y^3+x^3y)+C(6xy^2+x^4),\; \backslash ,$ where ''A'', ''B'', ''C'', ''D'' are arbitrary constants. The Euler–Tricomi equation is a limiting form of Chaplygin's equation. 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「Euler–Tricomi equation」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.