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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 Verlet integration ： ウィキペディア英語版 Verlet integration Verlet integration ((:vɛʁˈlɛ)) is a numerical method used to integrate Newton's equations of motion.〔 It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Delambre, and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by Cowell and Crommelin in 1909 to compute the orbit of Halley's Comet, and by Carl Størmer in 1907 to study the trajectories of electrical particles in a magnetic field (hence it is also called Störmer's method).〔 〕 The Verlet integrator provides good numerical stability, as well as other properties that are important in physical systems such as time-reversibility and preservation of the symplectic form on phase space, at no significant additional computational cost over the simple Euler method. ==Basic Störmer–Verlet== For a differential equation of second order of the type $\backslash ddot(t)=\backslash vec\; A(\backslash vec\; x(t))$ with initial conditions $\backslash vec\; x(t\_0)=\backslash vec\; x\_0$ and $\backslash dot(t\_0)=\backslash vec\; v\_0$, an approximate numerical solution $\backslash vec\; x\_n\backslash approx\; \backslash vec\; x(t\_n)$ at the times $t\_n=t\_0+n\backslash ,\backslash Delta\; t$ with step size $\backslash Delta\; t>0$ can be obtained by the following method: * set $\backslash vec\; x\_1=\backslash vec\; x\_0+\backslash vec\; v\_0\backslash ,\backslash Delta\; t+\backslash frac12\; A(\backslash vec\; x\_0)\backslash ,\backslash Delta\; t^2$ * for ''n=1,2,...'' iterate :::$$ \vec x_=2 \vec x_n- \vec x_+ A(\vec x_n)\,\Delta t^2. 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「Verlet integration」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.