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
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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.
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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
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*** LOAD THE PACKAGE
Needs["Calculus`VectorAnalysis`"];
*** TO CONVERT TO ANY MATHEMATICA COORDINATE SYSTEM
Thread[{x,y,z}-> CoordinatesToCartesian[{r,theta,phi},Spherical] ]
{x -> r Cos[phi] Sin[theta], y -> r Sin[phi] Sin[theta], z -> r Cos[theta]}
*** TO CONVERT FROM ANY MATHEMATICA COORDINATE SYSTEM
Thread[{r,theta,phi}-> CoordinatesFromCartesian[{x,y,z},Spherical] ]
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
Thread[{x,y,z}->
CoordinatesToCartesian[
Coordinates[EllipticCylindrical]
,EllipticCylindrical] ]
{x -> Cos[v] Cosh[u], y -> Sin[v] Sinh[u], z -> z}
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