Re: SYMBOLIC CONVERSION BETWEEN COORDINATE SYSTEMS:

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg464] Re: [mg451] SYMBOLIC CONVERSION BETWEEN COORDINATE SYSTEMS:
• From: olness at phyvms.physics.smu.edu
• Date: Mon, 13 Feb 1995 16:11:29 -0600

```---------------------------------------------------------
FROM: Luis Aguilar: SMTP%"aguilar at bufadora.astrosen.unam.mx"

SYMBOLIC CONVERSION BETWEEN COORDINATE SYSTEMS: I have a spatial scalar
function expressed in spherical coordinates. How can I get iso-surfaces ( or
iso-contours for 2D cuts), if the usual contouring routines assume that your
function is expressed in cartesian coordinates?

I also need to plot the vectorfield produced by the gradient of this function.
Although the `VectorAnalysis` package allows me to obtain the gradient, I'm
stuck with the conversion of coordinates problem when attempting to use the
PlotVectorField command.
---------------------------------------------------------
Luis, There is a useful trick for converting between coordinate
systems that should help solve part of your problem. You can find this trick,
and others,  in  Chapter 1 of MATHEMATICA FOR PHYSICS by Zimmerman & Olness
(Addison-Wesley Pub. Co.; MathSource Number: 0206-862)

Fredrick I. Olness, Olness at mail.physics.smu.edu
---------------------------------------------------------
Needs["Calculus`VectorAnalysis`"];

*** TO CONVERT TO ANY MATHEMATICA COORDINATE SYSTEM

{x -> r Cos[phi] Sin[theta], y -> r Sin[phi] Sin[theta], z -> r Cos[theta]}

*** TO CONVERT FROM ANY MATHEMATICA COORDINATE SYSTEM

2    2    2                           z
{r -> Sqrt[x  + y  + z ], theta -> ArcCos[------------------],
2    2    2
Sqrt[x  + y  + z ]
phi -> ArcTan[x, y]}

*** LET'S TRY SOMETHING EXOTIC
CoordinatesToCartesian[
Coordinates[EllipticCylindrical]
,EllipticCylindrical] ]

{x -> Cos[v] Cosh[u], y -> Sin[v] Sinh[u], z -> z}
---------------------------------------------------------

```

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