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 . Then we have:
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:
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}]