翻訳と辞書 Words near each other ・ Biplex aculeata ・ Biplex bozzettii ・ Biplex perca ・ Biplex pulchella ・ Biplob Bhattacharjee ・ Biplobi Bangla Congress ・ Biplot ・ Bipod ・ Bipod mast ・ Bipodtarini Devi ・ Bipolar ・ Bipolar (El Cuarteto de Nos album) ・ Bipolar (Up Dharma Down album) ・ Bipolar and Proud ・ Bipolar coordinates ・ Bipolar cylindrical coordinates ・ Bipolar disorder ・ Bipolar disorder in children ・ Bipolar disorder not otherwise specified ・ Bipolar disorder research ・ Bipolar Disorders (journal) ・ Bipolar electric motor ・ Bipolar electrochemistry ・ Bipolar encoding ・ Bipolar I disorder ・ Bipolar II disorder ・ Bipolar Integrated Technology ・ Bipolar junction transistor ・ Bipolar nebula ・ Bipolar neuron 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 Bipolar cylindrical coordinates ： ウィキペディア英語版 Bipolar cylindrical coordinates Bipolar cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional bipolar coordinate system in the perpendicular $z$-direction. The two lines of foci $F\_$ and $F\_$ of the projected Apollonian circles are generally taken to be defined by $x=-a$ and $x=+a$, respectively, (and by $y=0$) in the Cartesian coordinate system. The term "bipolar" is often used to describe other curves having two singular points (foci), such as ellipses, hyperbolas, and Cassini ovals. However, the term ''bipolar coordinates'' is never used to describe coordinates associated with those curves, e.g., elliptic coordinates. ==Basic definition== The most common definition of bipolar cylindrical coordinates $(\backslash sigma,\; \backslash tau,\; z)$ is :$$ x = a \ \frac :$$ y = a \ \frac :$$ z = \ z where the $\backslash sigma$ coordinate of a point $P$ equals the angle $F\_\; P\; F\_$ and the $\backslash tau$ coordinate equals the natural logarithm of the ratio of the distances $d\_$ and $d\_$ to the focal lines :$$ \tau = \ln \frac} (Recall that the focal lines $F\_$ and $F\_$ are located at $x=-a$ and $x=+a$, respectively.) Surfaces of constant $\backslash sigma$ correspond to cylinders of different radii :$$ x^ + \left( y - a \cot \sigma \right)^ = \frac \sigma} that all pass through the focal lines and are not concentric. The surfaces of constant $\backslash tau$ are non-intersecting cylinders of different radii :$$ y^ + \left( x - a \coth \tau \right)^ = \frac \tau} that surround the focal lines but again are not concentric. The focal lines and all these cylinders are parallel to the $z$-axis (the direction of projection). In the $z=0$ plane, the centers of the constant-$\backslash sigma$ and constant-$\backslash tau$ cylinders lie on the $y$ and $x$ axes, respectively. 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「Bipolar cylindrical coordinates」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.