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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 Gaussian polar coordinates ： ウィキペディア英語版 Gaussian polar coordinates In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In each of these spheres, every point can be carried to any other by an appropriate rotation about the center of symmetry. There are several different types of coordinate chart which are ''adapted'' to this family of nested spheres, each introducing a different kind of distortion. The best known alternative is the Schwarzschild chart, which correctly represents distances within each sphere, but (in general) distorts radial distances and angles. Another popular choice is the isotropic chart, which correctly represents angles (but in general distorts both radial and transverse distances). A third choice is the Gaussian polar chart, which correctly represents radial distances, but distorts transverse distances and angles. In all three possibilities, the nested geometric spheres are represented by coordinate spheres, so we can say that their ''roundness'' is correctly represented. ==Definition== In a Gaussian polar chart (on a static spherically symmetric spacetime), the line element takes the form :$ds^2\; =\; -f(r)^2\; \backslash ,\; dt^2\; +\; dr^2\; +\; g(r)^2\; \backslash ,\; \backslash left(\; d\backslash theta^2\; +\; \backslash sin(\backslash theta)^2\; \backslash ,\; d\backslash phi^2\; \backslash right),$ : Depending on context, it may be appropriate to regard f, g as undetermined functions of the radial coordinate. Alternatively, we can plug in specific functions (possibly depending on some parameters) to obtain an isotropic coordinate chart on a specific Lorentzian spacetime. 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「Gaussian polar coordinates」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.