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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 Hamilton's principle ： ウィキペディア英語版 Hamilton's principle In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action (see that article for historical formulations). It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the ''differential'' equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and has even been extended to quantum mechanics, quantum field theory and criticality theories. ==Mathematical formulation== Hamilton's principle states that the true evolution q(''t'') of a system described by ''N'' generalized coordinates q = (''q''1, ''q''2, ..., ''q''''N'') between two specified states q1 = q(''t''1) and q2 = q(''t''2) at two specified times ''t''1 and ''t''2 is a stationary point (a point where the variation is zero), of the action functional :$$ \mathcal() \ \stackrel\ \int_^ L(\mathbf(t),\dot,\dot. The action $\backslash mathcal$ is a functional, i.e., something that takes as its input a function and returns a single number, a scalar. In terms of functional analysis, Hamilton's principle states that the true evolution of a physical system is a solution of the functional equation =0 |border=2 |border colour = #50C878 |background colour = #ECFCF4}} 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「Hamilton'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.