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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 planar lamina ： ウィキペディア英語版 planar lamina In mathematics, a planar lamina is a closed set in a plane of mass $m$ and surface density $\backslash rho\backslash \; (x,y)$ such that: :$m\; =\; \backslash int\backslash int\_,\backslash frac\backslash right)$ where $M\_y$ moment of the entire lamina about the x-axis and $M\_x$ moment of the entire lamina about the y-axis. :$M\_y\; =\; \backslash lim\_\backslash ,\backslash sum\_^\backslash ,\backslash sum\_^\backslash ,x\backslash ,\backslash rho\backslash \; (x,y)\backslash ,\backslash Delta\backslash Alpha\; =\; \backslash iint\_\backslash ,\backslash sum\_^\backslash ,\backslash sum\_^\backslash ,y\backslash ,\backslash rho\backslash \; (x,y)\backslash ,\backslash Delta\backslash Alpha\; =\; \backslash iint\_\}\_+2y)|\_x^\backslash ,dx$ :$m=\backslash int\_0^2\; -4x^2-8x+32\backslash ,dx$ :$m=\; (\backslash frac-4x^2+32x)|\_0^2$ :$m=\; \backslash frac$ :$M\_y\; =\; \backslash int\_0^2+2xy)|\_x^\backslash ,dx$ :$M\_y=\backslash int\_0^2\; -4x^3-8x^2+32x\backslash ,dx$ :$M\_y=\; (-x^4-\backslash frac+16x^2)|\_0^2$ :$M\_y=\; \backslash frac$ :$M\_x\; =\; \backslash int\_0^2+\backslash frac-20x^2+80x\backslash right)\backslash right|\_0^2$ :$M\_x=\; \backslash frac$ center of mass is at the point :$\backslash left(\backslash frac\}\},\backslash frac\}\}\backslash right)=\backslash left(\backslash frac,\backslash frac\backslash right)$ Planar laminas can be used to determine moments of inertia, or center of mass. 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「planar lamina」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.