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单词 Bipolar coordinate system
释义

Bipolar coordinate system

中文百科

双极坐标系 Bipolar coordinates

(重定向自Bipolar coordinate system)

二维双极坐标系是一个正交坐标系。学术界上有三种常用的双极坐标系。除了在这里讨论的坐标系以外,另外两种是双心坐标系与双角坐标系。

这里所要讨论的双极坐标系创建于阿波罗尼奥斯圆。\sigma\,\! 的等值曲线是圆圈。 \tau\,\! 的等值曲线也是圆圈。两组圆圈互相垂直相交。双极坐标系有两个焦点 F_{1}\,\!F_{2}\,\! ,其直角坐标 (x,\ y)\,\! 通常分别设置为 ( - a,\ 0)\,\!(a,\ 0)\,\! 。所以,这两个焦点都处于直角坐标系的 x-轴。

双极坐标系是好几种三维正交坐标系的原始模。往 z-轴方向延伸,则可得到双极圆柱坐标系。绕着 x-轴旋转,即可得到双球坐标系。绕着 y-轴旋转,就可得到圆环坐标系。

英语百科

Bipolar coordinates 双极坐标系

(重定向自Bipolar coordinate system)
Bipolar coordinate system
Geometric interpretation of the bipolar coordinates. The angle σ is formed by the two foci and the point P, whereas τ is the logarithm of the ratio of distances to the foci. The corresponding circles of constant σ and τ are shown in red and blue, respectively, and meet at right angles (magenta box); they are orthogonal.

Bipolar coordinates are a two-dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. The first is based on the Apollonian circles. The curves of constant σ and of τ are circles that intersect at right angles. The coordinates have two foci F1 and F2, which are generally taken to be fixed at (−a, 0) and (a, 0), respectively, on the x-axis of a Cartesian coordinate system. The second system is two-center bipolar coordinates. There is also a third coordinate system that is based on two poles (biangular coordinates).

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更新时间:2025/6/21 22:34:24