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词汇 Elliptic cylindrical coordinates
分类 英语词汇 英语翻译词典
释义

Elliptic cylindrical coordinates

中文百科

椭圆柱坐标系

椭圆坐标系

椭圆柱坐标系是一种三维正交坐标系 。往 z-轴方向延伸二维的椭圆坐标系，则可得到椭圆柱坐标系；其坐标曲面是共焦的椭圆柱面与双曲柱面。椭圆柱坐标系的两个焦点 F_{1} 与 F_{2} 的直角坐标，分别设置为 ( - a,\ 0,\ 0) 与 (a,\ 0,\ 0) ，都处于直角坐标系的 x-轴。

英语百科

Elliptic cylindrical coordinates 椭圆柱坐标系

Coordinate surfaces of elliptic cylindrical coordinates. The yellow sheet is the prism of a half-hyperbola corresponding to ν=-45°, whereas the red tube is an elliptical prism corresponding to μ=1. The blue sheet corresponds to z=1. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (2.182, -1.661, 1.0). The foci of the ellipse and hyperbola lie at x = ±2.0.
椭圆坐标系

Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the perpendicular z-direction. Hence, the coordinate surfaces are prisms of confocal ellipses and hyperbolae. The two foci F_{1} and F_{2} are generally taken to be fixed at -a and +a, respectively, on the x-axis of the Cartesian coordinate system.
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