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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 Maupertuis' principle ： ウィキペディア英語版 Maupertuis' principle In classical mechanics, Maupertuis' principle (named after Pierre Louis Maupertuis), is that the path followed by a physical system is the one of least length (with a suitable interpretation of ''path'' and ''length''). It is a special case of the more generally stated principle of least action. Using the calculus of variations, it results in an integral equation formulation of the equations of motion for the system. ==Mathematical formulation== Maupertuis' principle states that the true path of a system described by $N$ generalized coordinates $\backslash mathbf\; =\; \backslash left(\; q\_,\; q\_,\; \backslash ldots,\; q\_\; \backslash right)$ between two specified states $\backslash mathbf\_$ and $\backslash mathbf\_$ is an extremum (i.e., a stationary point, a minimum, maximum or saddle point) of the abbreviated action functional :$$ \mathcal_() \ \stackrel\ \int \mathbf \cdot d\mathbf where $\backslash mathbf\; =\; \backslash left(\; p\_,\; p\_,\; \backslash ldots,\; p\_\; \backslash right)$ are the conjugate momenta of the generalized coordinates, defined by the equation :$$ p_ \ \stackrel\ \frac} where $L(\backslash mathbf,\backslash dot\_$. Note that the abbreviated action $\backslash mathcal\_$ is not a function, but a functional, i.e., something that takes as its input a function (in this case, the path between the two specified states) and returns a single number, a scalar. 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「Maupertuis' 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.