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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 Double pendulum ： ウィキペディア英語版 Double pendulum In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.〔Levien RB and Tan SM. Double Pendulum: An experiment in chaos.''American Journal of Physics'' 1993; 61 (11): 1038〕 The motion of a double pendulum is governed by a set of coupled ordinary differential equations. For certain energies its motion is chaotic. ==Analysis and interpretation== Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to the vertical plane. In the following analysis, the limbs are taken to be identical compound pendulums of length $\backslash ell$ and mass $m$, and the motion is restricted to two dimensions. In a compound pendulum, the mass is distributed along its length. If the mass is evenly distributed, then the center of mass of each limb is at its midpoint, and the limb has a moment of inertia of $\backslash textstyle\; I=\backslash frac\; m\; \backslash ell^2$ about that point. It is convenient to use the angles between each limb and the vertical as the generalized coordinates defining the configuration of the system. These angles are denoted θ1 and θ2. The position of the center of mass of each rod may be written in terms of these two coordinates. If the origin of the Cartesian coordinate system is taken to be at the point of suspension of the first pendulum, then the center of mass of this pendulum is at: :$$ x_1 = \frac \sin \theta_1, :$$ y_1 = -\frac \cos \theta_1 and the center of mass of the second pendulum is at :$$ x_2 = \ell \left ( \sin \theta_1 + \frac \sin \theta_2 \right ), :$$ y_2 = -\ell \left ( \cos \theta_1 + \frac \cos \theta_2 \right ). This is enough information to write out the Lagrangian. 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「Double pendulum」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.