| 翻訳と辞書 |
| line element ： ウィキペディア英語版 |
line element
In geometry, the line element or length element can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parameterizing the given curve by Frenet–Serret formulas. As such, a ''line element'' is then naturally a function of the metric tensor, and can be related to the curvature tensor. It is usually denoted by ''s'' or ', and differentials of this are then written ''ds'' or ''d''.
Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved manifold with a metric tensor. For example, if a massive object causes some curvature in spacetime, the trajectory of an object with negligible mass over that curvature would follow the line element according to the geodesic equation.〔Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, ISBN 0-7167-0344-0〕
==General formulation==
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「line element」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.
|
|