Mathematica 8: Convert from cartesian to spherical coordinates

Question

I just started using Mathematica and came across a problem. I would like to solve more elegantly. I have measurement data in {x,y,z} form and want to transform these into sperical coordinates. I know how to do it using simple functions. But the code gets ugly. I would like something like:

v={x,y,z}
TranformSpherical[v]

I have looked in the documentation and only found something for version 9, I am using 8 and it did not work when I tried it. Also I have not found a clear solution anywhere else. Hope someone here knows a simple solution to the probem.

Answer 1

The equations are given on Wikipedia and are simple function evaluations. What's stopping you from simply computing them, and how does it get ugly?

Make sure to use ArcTan[x, y] in Mathematica, which computes the four-quadrant arctangent. For more information see the article about atan2.

Answer 2

In version 9

CoordinateTransformData["Cartesian" -> "Spherical", "Mapping", {x, y, z}]

gives you {Sqrt[x^2 + y^2 + z^2], ArcTan[z, Sqrt[x^2 + y^2]], ArcTan[x, y]}

which expresses the three spherical coordinates in terms of {x,y,z}

CoordinateTransform["Cartesian" -> "Spherical", {x, y, z}]

will give you the same thing, but can also be used for conversion. If you have a list {{x0,y0,z0},{x1,y1,z1},...} of Cartesian coordinates, you can apply CoordinateTransform like this

cartesianList = RandomReal[{0, 1}, {4, 3}];

CoordinateTransform["Cartesian" -> "Spherical", #] & /@ cartesianList 

In earlier versions

<< Calculus`VectorAnalysis`

SetCoordinates[Spherical]

There is a notebook at the mathworld.wolfram.com site page for Spherical Coordinates. Close to the beginning is an example for what you are doing.