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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 Meissner equation ： ウィキペディア英語版 Meissner equation The Meissner equation is a linear ordinary differential equation that is a special case of Hill's equation with the periodic function given as a square wave.〔 〕 〔 〕 There are many ways to write the Meissner equation. One is as : $\backslash frac\; +\; (\backslash alpha^2\; +\; \backslash omega^2\; \backslash sgn\; \backslash cos(t))y\; =\; 0$ or : $\backslash frac\; +\; (\; 1\; +\; r\; f(t;a,b)\; )\; y\; =\; 0$ where : $f(t;a,b)\; =\; -1\; +\; 2\; H\_a(\; t\; \backslash mod\; (a+b)\; )$ and $H\_c(t)$ is the Heaviside function shifted to $c$. Another version is : $\backslash frac\; +\; \backslash left(\; 1\; +\; r\; \backslash frac\; \backslash right)\; y\; =\; 0.$ The Meissner equation was first studied as a toy problem for certain resonance problems. It is also useful for understand resonance problems in evolutionary biology. Because the time-dependence is piecewise linear, many calculations can be performed exactly, unlike for the Mathieu equation. When $a\; =\; b\; =\; 1$, the Floquet exponents are roots of the quadratic equation : $\backslash lambda^2\; -\; 2\; \backslash lambda\; \backslash cosh(\backslash sqrt)\; \backslash cos(\backslash sqrt)\; +\; 1\; =\; 0\; .$ The determinant of the Floquet matrix is 1, implying that origin is a center if and a saddle node otherwise. == References == 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「Meissner 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.