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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 Mass matrix ： ウィキペディア英語版 Mass matrix In analytical mechanics, the mass matrix is a symmetric matrix ''M'' that expresses the connection between the time derivative $\backslash dot\; q$ of the generalized coordinate vector ''q'' of a system and the kinetic energy ''T'' of that system, by the equation :$T\; =\; \backslash frac\; \backslash dot\; q^\backslash mathrm\; M\; \backslash dot\; q$ where $\backslash dot\; q^\backslash mathrm$ denotes the transpose of the vector $\backslash dot\; q$.〔 This equation is analogous to the formula for the kinetic energy of a particle with mass $m$ and velocity ''v'', namely :$T\; \backslash ;=\backslash ;\; \backslash frac\; m|v|^2\; \backslash ;=\backslash ;\; \backslash frac\; v\backslash cdot\; m\; v$ and can be derived from it, by expressing the position of each particle of the system in terms of ''q''. In general, the mass matrix ''M'' depends on the state ''q'', and therefore varies with time. Lagrangian mechanics yields an ordinary differential equation (actually, a system of coupled differential equations) that describes the evolution of a system in terms of an arbitrary vector of generalized coordinates that completely defines the position of every particle in the system. The kinetic energy formula above is one term of that equation, that represents the total kinetic energy of all the particles. ==Examples== 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「Mass matrix」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.