长球面坐标系

In principle, a definition of prolate spheroidal coordinates could be degenerate. In other words, a single set of coordinates might correspond to two points in Cartesian coordinates; this is illustrated here with two black spheres, one on each sheet of the hyperboloid and located at (x, y, ±z). However, neither of the definitions presented here are degenerate.

长球面坐标系是一种三维正交坐标系。设置二维椭圆坐标系包含于 xz-平面；两个焦点 $F_{1}$ 与 $F_{2}$ 的直角坐标分别为 $(0,\ 0,\ - a)$ 与 $(0,\ 0,\ a)$ 。将椭圆坐标系绕着 z-轴旋转，则可以得到长球面坐标系。（假若，绕着 y-轴旋转，则可以得到扁球面坐标系。）椭圆坐标系的两个焦点，包含于 z-轴。长球面坐标系可以被视为椭球坐标系的极限案例，其两个最短的半轴的长度相同。

单词	Prolate spheroidal coordinates
释义	Prolate spheroidal coordinates 中文百科长球面坐标系长球面坐标系是一种三维正交坐标系。设置二维椭圆坐标系包含于 xz-平面；两个焦点 $F_{1}$ 与 $F_{2}$ 的直角坐标分别为 $(0,\ 0,\ - a)$ 与 $(0,\ 0,\ a)$ 。将椭圆坐标系绕着 z-轴旋转，则可以得到长球面坐标系。（假若，绕着 y-轴旋转，则可以得到扁球面坐标系。）椭圆坐标系的两个焦点，包含于 z-轴。长球面坐标系可以被视为椭球坐标系的极限案例，其两个最短的半轴的长度相同。英语百科 Prolate spheroidal coordinates 长球面坐标系 Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates. Prolate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two smallest principal axes are equal in length.
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Prolate spheroidal coordinates

长球面坐标系

Prolate spheroidal coordinates 长球面坐标系