# Profile Curve

• Mar 11th 2011, 01:06 PM
Student57
Profile Curve
This is translated from my own language, so feel free to correct me if I'm using a wrong translation.

A profile curve in (x, z)-plan is given by the graph of the function z = ln (x), where
x $\displaystyle \epsilon$ [1, 2]. The profile curve is rotated the angle $\displaystyle Pi$ around z-axis counterclockwise as seen from the z-axis'
positive end. This yields the rotation surface F.

Find a parametrization for the profile curve and F.
• Mar 13th 2011, 02:01 PM
zzzoak
$\displaystyle F=ln(\sqrt{x^2+y^2})$

In cylindrical coordinates

$\displaystyle F=ln \ r \ .$
• Mar 14th 2011, 01:18 PM
Student57
Still need to find r(u,v) any help here? (Thinking)
• Mar 14th 2011, 02:31 PM
zzzoak
If this helps:

$\displaystyle u=x$

$\displaystyle v=y$

$\displaystyle F=ln \sqrt{u^2+v^2}$

where

$\displaystyle v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ .$
• Mar 15th 2011, 03:11 AM
Student57
I think I'm being misunderstood.
I need to find the parametrization/parametric equation for the profile curve and F.

I was given this general equation:
$\displaystyle r(u,v)=(x(u,v),y(u,v)$