Write the equations of a surface of revolution with axis OZ:
A) the Torus obtained by a rotation of a circle x= a + b*sin(u), y= 0, z = b*sin(u)
0 < b < a
B) the pseduosphere obtained by the rotation of a tractrix x= a*sin(u), y=0, z= a*(log(tan(u/2) + cos(u))
C) the catenoid obtained by the rotation of the catenary x = a*cosh(u/a) y=0, z= u.
Unfortuantly my professor gave the questions from another text, whose 1st chapter covers this material; however, it is not covered in my material (he claims that we should have enough intuition to figure this out, however, I don't seem to have it.
But besides that point, I was able to find the following general standard form of parametrization of a surface of revolution on mathworld's website:
The Attempt at a Solution
As hinted at above, I don't quite have the background to tackle this problem. At the moment I have written down the standard form, as above; however, I don't know what the functions phi or psi are, nor do I have much of an idea of how to find them, so if there are any ideas of where to go with this.
Or I could be looking at this the entirely wrong way. So any help would be appreached so I can get this started.
(Oh and the website that I snaged the equation from is as follows:
Thanks in advanced for any suggestions on where to get started.