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单词 Cylindrical coordinate system
释义

Cylindrical coordinate system

中文百科

圆柱坐标系

圆柱坐标系（cylindrical coordinate system）是一种三维坐标系统。它是二维极坐标系往 z-轴的延伸。添加的第三个坐标 z 专门用来表示 P 点离 xy-平面的高低。按照国际标准化组织创建的约定 (ISO 31-11) ，径向距离、方位角、高度，分别标记为 (\rho,\ \phi,\ z) 。

如图右，P 点的圆柱坐标是 (\rho,\ \phi,\ z) 。

  • \rho 是 P 点与 z-轴的垂直距离。
  • \phi 是线 OP 在 xy-面的投影线与正 x-轴之间的夹角。
  • z 与直角坐标的 z 等值。
英语百科

Cylindrical coordinate system 圆柱坐标系

A cylindrical coordinate system with origin O, polar axis A, and longitudinal axis L. The dot is the point with radial distance ρ = 4, angular coordinate φ = 130°, and height z = 4.
The coordinate surfaces of the cylindrical coordinates (ρ, φ, z). The red cylinder shows the points with ρ=2, the blue plane shows the points with z=1, and the yellow half-plane shows the points with φ=−60°. The z-axis is vertical and the x-axis is highlighted in green. The three surfaces intersect at the point P with those coordinates (shown as a black sphere); the Cartesian coordinates of P are roughly (1.0, −1.732, 1.0).
Cylindrical coordinate surfaces. The three orthogonal components, ρ (green), φ (red), and z (blue), each increasing at a constant rate. The point is at the intersection between the three colored surfaces.

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.
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更新时间：2025/6/21 0:23:46