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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 Pendulum (mathematics) ： ウィキペディア英語版 Pendulum (mathematics) The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle oscillations. == Simple gravity pendulum == A so-called "simple pendulum" is an idealization of a "real pendulum" but in an isolated system using the following assumptions: * The rod or cord on which the bob swings is massless, inextensible and always remains taut; * The bob is a point mass; * Motion occurs only in two dimensions, i.e. the bob does not trace an ellipse but an arc. * The motion does not lose energy to friction or air resistance. * The gravitational field is uniform. * The support does not move. The differential equation which represents the motion of a simple pendulum is where $g$ is acceleration due to gravity, $\backslash ell$ is the length of the pendulum, and $\backslash theta$ is the angular displacement. , where $\backslash mathbf$ is the length vector of the pendulum and $\backslash mathbf$ is the force due to gravity. For now just consider the magnitude of the torque on the pendulum. :$\backslash mathbf\; =\; -mg\; l\; \backslash sin\backslash theta,$ where $m$ is the mass of the pendulum, $g$ is the acceleration due to gravity, $l$ is the length of the pendulum and $\backslash theta$ is the angle between the length vector and the force due to gravity. Next rewrite the angular momentum. :$\backslash mathbf\; =\; \backslash mathbf\; =\; m\backslash mathbf$. Again just consider the magnitude of the angular momentum. :$\backslash mathbf\; =\; mr^2\; \backslash omega\; =\; m\; l^2$. and its time derivative :$\backslash mathbf\; =\; m\; l^2$, According to $\backslash over\; dt\}\; \}$, we can get by comparing the magnitudes :$-mgl\; \backslash sin\backslash theta\; =\; m\; l^2$, thus: :$+\; \backslash sin\backslash theta\; =\; 0,$ which is the same result as obtained through force analysis. }} |} = \sqrt \\ & = 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「Pendulum (mathematics)」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.