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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 Duffing equation ： ウィキペディア英語版 Duffing equation The Duffing equation (or Duffing oscillator), named after Georg Duffing, is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by :$\backslash ddot\; +\; \backslash delta\; \backslash dot\; +\; \backslash alpha\; x\; +\; \backslash beta\; x^3\; =\; \backslash gamma\; \backslash cos\; (\backslash omega\; t)\backslash ,$ where the (unknown) function ''x''=''x''(''t'') is the displacement at time ''t'', $\backslash dot$ is the first derivative of ''x'' with respect to time, i.e. velocity, and $\backslash ddot$ is the second time-derivative of ''x'', i.e. acceleration. The numbers $\backslash delta$, $\backslash alpha$, $\backslash beta$, $\backslash gamma$ and $\backslash omega$ are given constants. The equation describes the motion of a damped oscillator with a more complicated potential than in simple harmonic motion (which corresponds to the case β=δ=0); in physical terms, it models, for example, a spring pendulum whose spring's stiffness does not exactly obey Hooke's law. The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. Moreover, the Duffing system presents in the frequency response the jump resonance phenomenon that is a sort of frequency hysteresis behaviour. ==Parameters== * $\backslash delta$ controls the size of the damping. * $\backslash alpha$ controls the size of the stiffness. * $\backslash beta$ controls the amount of non-linearity in the restoring force. If $\backslash beta=0$, the Duffing equation describes a damped and driven simple harmonic oscillator. * $\backslash gamma$ controls the amplitude of the periodic driving force. If $\backslash gamma=0$ we have a system without driving force. * $\backslash omega$ controls the frequency of the periodic driving force. 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「Duffing 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.