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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 gyration tensor ： ウィキペディア英語版 gyration tensor In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles :$$ S_ \ \stackrel\ \frac\sum_^ r_^ r_^ where $r\_^$ is the $\backslash mathrm^$ of the $\backslash mathrm^\; \backslash mathbf^\; =\; 0$ i.e. in the system of the center of mass $r\_$. Where :$$ r_=\frac\sum_^ \mathbf^ Another definition, which is mathematically identical but gives an alternative calculation method, is: :$$ S_ \ \stackrel\ \frac^\sum_^ (r_^ - r_^) (r_^ - r_^) Therefore, the x-y component of the gyration tensor for particles in Cartesian coordinates would be: :$$ S_ = \frac^\sum_^ (x_ - x_) (y_ - y_) In the continuum limit, :$$ S_ \ \stackrel\ \dfrac) \ r_ r_})} where $\backslash rho(\backslash mathbf)$ represents the number density of particles at position $\backslash mathbf$. Although they have different units, the gyration tensor is related to the moment of inertia tensor. The key difference is that the particle positions are weighted by mass in the inertia tensor, whereas the gyration tensor depends only on the particle positions; mass plays no role in defining the gyration tensor. ==Diagonalization== Since the gyration tensor is a symmetric 3x3 matrix, a Cartesian coordinate system can be found in which it is diagonal :$$ \mathbf = \begin \lambda_^ & 0 & 0 \\ 0 & \lambda_^ & 0 \\ 0 & 0 & \lambda_^ \end where the axes are chosen such that the diagonal elements are ordered $\backslash lambda\_^\; \backslash leq\; \backslash lambda\_^\; \backslash leq\; \backslash lambda\_^$. These diagonal elements are called the principal moments of the gyration tensor. 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「gyration tensor」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.