Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Coordinate Systems

坐标系统
Rectangular Coordinates
矩形坐标
Cylindrical Polar Coordinates
圆柱坐标
Spherical Polar Coordinates
球坐标
Applications:
Distance between points
应用:点之间的距离
Applications:
Cylindrical capacitor
Electric field of line charge.
应用:圆柱形电容器 电场线电荷的电场。
Applications:
Hydrogen Schrodinger Equation
Maxwell speed distribution
Electric potential of sphere
应用:氢的薛定谔方程 马克斯韦速度分布 电势
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Rectangular Coordinates

矩形坐标
The most common coordinate system for representing positions in space is one based on three perpendicular spatial axes generally designated x, y, and z.

Any point P may be represented by three signed numbers, usually written (x, y, z) where the coordinate is the perpendicular distance from the plane formed by the other two axes.

任何点P都可以用三个带符号的数表示,通常写作(x, y, z),其中坐标是该点到由另外两个轴所形成的平面的垂直距离。

Often positions are specified by a position vector r which can be expressed in terms of the coordinate values and associated unit vectors.

位置通常由位置矢量 r 表示,该矢量可以表示为坐标值和相关单位矢量的组合。

Although the entire coordinate system can be rotated, the relationship between the axes is fixed in what is called a right-handed coordinate system.

尽管整个坐标系可以旋转,但坐标轴之间的关系在所谓的右手法坐标系中是固定的。

For the display of some kinds of data,it may be convenient to have different scales for the different axes, but for the purpose of mathematical operations with the coordinates, it is necessary for the axes to have the same scales. The term "Cartesian coordinates" is used to describe such systems, and the values of the three coordinates unambiguously locate a point in space. In such a coordinate system you can calculate the distance between two points and perform operations like axis rotations without altering this value.

The distance between any two points in rectangular coordinates can be found from the distance relationship.

矩形坐标系中任意两点之间的距离可通过距离关系确定。
对于显示某些类型的数据来说,可能方便不同轴使用不同的刻度,但为了进行坐标运算,轴必须具有相同的刻度。术语“笛卡尔坐标”用于描述这样的系统,三个坐标的值可以唯一确定空间中的一个点。在这样的坐标系中,你可以计算两点之间的距离,并进行如轴旋转等操作,而不会改变这个值。


Operations in Cartesian coordinates.

直角坐标系中的运算
在空间中表示位置最常用的坐标系是基于三个互相垂直的空间轴的坐标系,通常分别标记为x、y和z。
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Operations in Cartesian Coordinates

直角坐标系中的运算
Distance between points
点之间的距离
Vector calculus operations

Divergence

散度

Gradient

梯度

Curl

旋度

LaPlacian

拉普拉斯算子

矢量微积分运算
Index
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HyperPhysics****HyperMath*****Geometry
HyperPhysics **** HyperMath ***** 几何
R Nave
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