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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 D'Alembert's principle ： ウィキペディア英語版 D'Alembert's principle D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert. It is the dynamic analogue to the ''principle of virtual work for applied forces'' in a static system and in fact is more general than Hamilton's principle, avoiding restriction to holonomic systems. A holonomic constraint depends only on the coordinates and time. It does not depend on the velocities. If the negative terms in accelerations are recognized as ''inertial forces'', the statement of d'Alembert's principle becomes ''The total virtual work of the impressed forces plus the inertial forces vanishes for reversible displacements''. The principle does not apply for irreversible displacements, such as sliding friction, and more general specification of the irreversibility is required. The principle states that the sum of the differences between the forces acting on a system of mass particles and the time derivatives of the momenta of the system itself along any virtual displacement consistent with the constraints of the system, is zero. Thus, in symbols d'Alembert's principle is written as following, :$\backslash sum\_\; (\; \backslash mathbf\; \_\; -\; m\_i\; \backslash mathbf\_i\; )\backslash cdot\; \backslash delta\; \backslash mathbf\; r\_i\; =\; 0,$ where : This above equation is often called d'Alembert's principle, but it was first written in this variational form by Joseph Louis Lagrange.〔Arnold Sommerfeld (1956), ''Mechanics: Lectures on Theoretical Physics'', Vol 1, p. 53〕 D'Alembert's contribution was to demonstrate that in the totality of a dynamic system the forces of constraint vanish. That is to say that the generalized forces $\_$ need not include constraint forces. It is equivalent to the somewhat more cumbersome Gauss's principle of least constraint. ==General case with changing masses== The general statement of d'Alembert's principle mentions "the time derivatives of the momenta of the system". The momentum of the ''i''-th mass is the product of its mass and velocity: :$\backslash mathbf\; p\_i\; =\; m\_i\; \backslash mathbf\; v\_i$ and its time derivative is :$\backslash dot\; =\; \backslash dot\_i\; \backslash mathbf\_i\; +\; m\_i\; \backslash dot\_i\}\; =\; m\_i\; \backslash dot\_i$, which appears in the formula given above. However, some applications involve changing masses (for example, chains being rolled up or being unrolled) and in those cases both terms $\backslash dot\_i\; \backslash mathbf\_i$ and $m\_i\; \backslash dot\; (\; \backslash mathbf\; \_\; -\; m\_i\; \backslash mathbf\_i\; -\; \backslash dot\_i\; \backslash mathbf\_i)\backslash cdot\; \backslash delta\; \backslash mathbf\; r\_i\; =\; 0.$ 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「D'Alembert's principle」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.