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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 Method of averaging ： ウィキペディア英語版 Method of averaging In the study of dynamical systems, the method of averaging is used to study certain time-varying systems by analyzing easier, time-invariant systems obtained by averaging the original system. == Definition == Consider a general, nonlinear dynamical system $\backslash dot\; =\; \backslash epsilon\; f(\; t,\; x\; ,\; \backslash epsilon\; )$ where $f(t,x)$ is periodic in $t$ with period $T$. The evolution of this system is said to occur in two timescales: a fast oscillatory one associated with the presence of $t$ in $f$ and a slow one associated with the presence of $\backslash epsilon$ in front of $f$. The corresponding (leading order in $\backslash epsilon$) averaged system is $\backslash dot^\; =\; \backslash epsilon\; \backslash frac\backslash int\_^f(\backslash tau,x,0)\; d\backslash tau\; =\; \backslash tilde(x^).$ Averaging mods out the fast oscillatory dynamics by averaging their effect (through time integration - see the formula above). In this way, the mean (or long-term) behavior of the system is retained in the form of the dynamical equation for the evolution for $x^$. Standard methods for time-invariant (autonomous) systems may then be employed to analyze the equilibria (and their stability) as well as other dynamical objects of interest present in the phase space of the averaged system. 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「Method of averaging」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.