翻訳と辞書 Words near each other ・ Introduction of the Bundesliga ・ Introduction to a Waltz ・ Introduction to Algorithms ・ Introduction to Arithmetic ・ Introduction to Automata Theory, Languages, and Computation ・ Intriguer ・ Intrinsa ・ Intrinsic (album) ・ Intrinsic activity ・ Intrinsic and extrinsic aging ・ Intrinsic and extrinsic properties ・ Intrinsic and extrinsic properties (philosophy) ・ Intrinsic apoptosis ・ Intrinsic brightness ・ Intrinsic dimension ・ Intrinsic equation ・ Intrinsic factor ・ Intrinsic finality ・ Intrinsic flat distance ・ Intrinsic fraud ・ Intrinsic function ・ Intrinsic happiness ・ Intrinsic hyperpolarizability ・ Intrinsic immunity ・ Intrinsic low-dimensional manifold ・ Intrinsic metric ・ Intrinsic Noise Analyzer ・ Intrinsic parity ・ Intrinsic pathway ・ Intrinsic safety Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Intrinsic equation ： ウィキペディア英語版 Intrinsic equation In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system. The intrinsic quantities used most often are arc length $s$, tangential angle $\backslash theta$, curvature $\backslash kappa$ or radius of curvature, and, for 3-dimensional curves, torsion $\backslash tau$. Specifically: * The natural equation is the curve given by its curvature and torsion. * The Whewell equation is obtained as a relation between arc length and tangential angle. * The Cesàro equation is obtained as a relation between arc length and curvature. The equation of a circle (including a line) for example is given by the equation $\backslash kappa(s)\; =\; \backslash tfrac$ where $s$ is the arc length, $\backslash kappa$ the curvature and $r$ the radius of the circle. These coordinates greatly simplify some physical problem. For elastic rods for example, the potential energy is given by :$E=\; \backslash int\_0^L\; B\; \backslash kappa^2(s)ds$ where $B$ is the bending modulus $EI$. Moreover, as $\backslash kappa(s)\; =\; d\backslash theta/ds$, elasticity of rods can be given a simple variational form. ==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「Intrinsic equation」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.