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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 Virtual displacement ： ウィキペディア英語版 Virtual displacement In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement δr''i'' "is an assumed infinitesimal change of system coordinates occurring while time is held constant. It is called virtual rather than real since no actual displacement can take place without the passage of time." Also, virtual displacements are spatial displacements exclusively - time is fixed while they occur. When computing virtual differentials of quantities that are functions of space and time coordinates, no dependence on time is considered (formally equivalent to saying ''δt'' = 0). In modern terminology virtual displacement is a tangent vector to the manifold representing the constraints at a fixed time. Unlike regular displacement which arises from differentiating with respect to time parameter ''t'' along the path of the motion (thus pointing in the direction of the motion), virtual displacement arises from differentiating with respect to the parameter ''ε'' enumerating paths of the motion varied in a manner consistent with the constraints (thus pointing at a fixed time in the direction tangent to the constraining manifold). The symbol ''δ'' is traditionally used to denote the corresponding derivative :$\backslash delta\; =\; \backslash left.\; \backslash frac\backslash right|\_\backslash ,.$ ==Comparison between virtual and actual displacements== The total differential of any set of system position vectors, r''i'', that are functions of other variables :$\backslash lbrace\; q\_1,\; q\_2,\; ...,\; q\_m\backslash rbrace\backslash ,$ and time ''t'' may be expressed as follows:〔 :$d\; \backslash mathbf\_i\; =\; \backslash frac\; d\; t\; +\; \backslash sum\_^m\; \backslash frac\; d\; q\_j\backslash ,$ If, instead, we want the virtual displacement (virtual differential displacement), then〔 :$\backslash delta\; \backslash mathbf\_i\; =\; \backslash sum\_^m\; \backslash frac\; \backslash delta\; q\_j\backslash ,$ This equation is used in Lagrangian mechanics to relate generalized coordinates, ''qj'', to virtual work, ''δW'', and generalized forces, ''Qj''. 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「Virtual displacement」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.