翻訳と辞書
Words near each other
・ Line D (Rome Metro)
・ Line dance
・ Line Daugaard
・ Line Defense
・ Line Delimited JSON
・ Line Describing a Cone
・ Line discipline
・ Line doubler
・ Line drawing
・ Line drawing algorithm
・ Line drive
・ Line driver
・ Line E (Buenos Aires Underground)
・ Line echo wave pattern
・ Line editor
Line element
・ Line Engaged
・ Line engraving
・ Line F (Buenos Aires Underground)
・ Line field
・ Line filter
・ Line fitting
・ Line Focus Principle
・ Line function
・ Line G (Buenos Aires Underground)
・ Line graph
・ Line graph of a hypergraph
・ Line group
・ Line H (Buenos Aires Underground)
・ Line H7 (Budapest HÉV)


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

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.