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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 Variational vector field ： ウィキペディア英語版 Variational vector field In the mathematical fields of the calculus of variations and differential geometry, the variational vector field is a certain type of vector field defined on the tangent bundle of a differentiable manifold which gives rise to variations along a vector field in the manifold itself. Specifically, let ''X'' be a vector field on ''M''. Then ''X'' generates a one-parameter group of local diffeomorphisms ''Fl''Xt, the flow along ''X''. The differential of ''Fl''Xt gives, for each ''t'', a mapping :$d\backslash mathrm\_X^t\; :\; TM\; \backslash to\; TM$ where ''TM'' denotes the tangent bundle of ''M''. This is a one-parameter group of local diffeomorphisms of the tangent bundle. The variational vector field of ''X'', denoted by ''T''(''X'') is the tangent to the flow of ''d Fl''Xt. ==References== * 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「Variational vector field」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.