Originally Posted by

**choccookies** hi, thanks for your help.

yeah i didnt know how to type the real symbols for the sphericals. Oh also I forgot to put the conditions;

E>= 0, Pi>=T>=0, 2Pi>=Q>=0

How would I draw the surface? If E was constant I;d get

x=sinTcosQ

y=sintTsinQ

z=cosT

This seems too tricky to plot?

Build it up piece by piece. First let $\displaystyle t=\pi/2$. Then we have:

$\displaystyle x=k\cos(q)$

$\displaystyle y=k\sin(q)$

$\displaystyle z=0$

so that's obviously some curve in the x-y plane right? And the sine and cosine thing means it's a circle with radius k. So draw that one. Now, how about letting t=0? Then do a few more and see what it starts looking like. Also, compare your user-defined coordinate system with the standard spherical coordinate transformations and note the similarities:

$\displaystyle x=\rho\sin(\phi)\cos(\theta)$

$\displaystyle y=\rho\sin(\phi)\sin(\theta)$

$\displaystyle z=\rho\cos(\phi)$

That's kinda' tough for me. Here's what it looks like in Mathematica as e is varied between 0 and 1. Try and get a machine to run the code on it, see what's happening, then try and explain it analytically:

Code:

Manipulate[
ParametricPlot3D[{Cosh[e] Sin[t] Cos[q], Cosh[e] Sin[t] Sin[q],
Sinh[e] Cos[t]}, {t, 0, \[Pi]}, {q, 0, 2 \[Pi]},
PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}}], {e, 0, 1}]