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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 Acceleration (differential geometry) ： ウィキペディア英語版 Acceleration (differential geometry) In mathematics and physics, acceleration is the rate of change of velocity of a curve with respect to a given linear connection. This operation provides us with a measure of the rate and direction of the "bend". ==Formal definition== Consider a differentiable manifold $M$ with a given connection $\backslash Gamma$. Let $\backslash gamma\; \backslash colon\backslash R\; \backslash to\; M$ be a curve in $M$ with tangent vector, i.e. velocity, $(t)$. The acceleration vector of $\backslash gamma$ is defined by $\backslash nabla\_$, where $\backslash nabla$ denotes the covariant derivative associated to $\backslash Gamma$. It is a covariant derivative along $\backslash gamma$, and it is often denoted by :$\backslash nabla\_\; =\backslash frac.$ The concept of acceleration is a covariant derivative concept. In other words, in order to define acceleration an additional structure on $M$ must be given. 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「Acceleration (differential geometry)」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.