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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 vector spherical harmonics ： ウィキペディア英語版 vector spherical harmonics In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for the use with vector fields. ==Definition== Several conventions have been used to define the VSH.〔 R.G. Barrera, G.A. Estévez and J. Giraldo, ''Vector spherical harmonics and their application to magnetostatics'', Eur. J. Phys. 6 287-294 (1985)〕〔B. Carrascal, G.A. Estevez, P. Lee and V. Lorenzo '' Vector spherical harmonics and their application to classical electrodynamics'', Eur. J. Phys., 12, 184-191 (1991)〕〔 E. L. Hill, ''The theory of Vector Spherical Harmonics'', Am. J. Phys. 22, 211-214 (1954)〕〔 E. J. Weinberg, ''Monopole vector spherical harmonics'', Phys. Rev. D. 49, 1086-1092 (1994)〕〔P.M. Morse and H. Feshbach, ''Methods of Theoretical Physics, Part II'', New York: McGraw-Hill, 1898-1901 (1953)〕 We follow that of Barrera ''et al.''. Given a scalar spherical harmonic $Y\_(\backslash theta,\backslash varphi)$ we define three VSH: * $\backslash mathbf\_\; =\; Y\_\backslash hat\_\; =\; r\backslash nabla\; Y\_$ * $\backslash mathbf\_\; =\; \backslash vec$ being $\backslash hat\}$ the position vector of the point with spherical coordinates $r$,$\backslash theta$ and$\backslash phi$. The radial factors are included to guarantee that the dimensions of the VSH are the same as the ordinary spherical harmonics and that the VSH do not depend on the radial spherical coordinate. The interest of these new vector fields is to separate the radial dependence from the angular one when using spherical coordinates, so that a vector field admits a multipole expansion : $\backslash mathbf=\backslash sum\_^\backslash infty\backslash sum\_^l\backslash left(E^r\_(r)\backslash mathbf\_+E^\_(r)\backslash mathbf\_+E^\_(r)\backslash mathbf\_\backslash right)$ The labels on the components reflect that $E^r\_$ is the radial component of the vector field, while $E^\_$ and $E^\_$ are transverse components. 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「vector spherical harmonics」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.