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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 Clairaut's relation ： ウィキペディア英語版 Clairaut's relation Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry. The formula relates the distance ''r''(''t'') from a point on a great circle of the unit sphere to the ''z''-axis, and the angle ''θ''(''t'') between the tangent vector and the latitudinal circle: :$r(t)\; \backslash cos\; \backslash theta(t)\; =\; \backslash text.\backslash ,$ The relation remains valid for a geodesic on an arbitrary surface of revolution. A formal mathematical statement of Clairaut's relation is: Pressley (p. 185) explains this theorem as an expression of conservation of angular momentum about the axis of revolution when a particle slides along a geodesic under no forces other than those that keep it on the surface. ==References== *M. do Carmo, ''Differential Geometry of Curves and Surfaces'', page 257. 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「Clairaut's relation」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.