# Transforme kinetic energy in parabolical cyndrical coordinates

1. Sep 4, 2012

### arantxa.ceped

1. The problem statement, all variables and given/known data

The transformation from cartesian coordinates to cylindrical coordinates is given by:

x = 1/2 (u2 - v2), y=uv, z=z

2. Relevant equations

compute the kinetic energy 1/2mv2 in parabolic cylindrical coordinates

3. The attempt at a solution

Any ideas??

2. Sep 5, 2012

### clamtrox

In carteesian coordinates, $E = \frac{1}{2} m v^2 = \frac{1}{2} m (\dot{x}^2+\dot{y}^2+\dot{z}^2)$. You want to write this into a form with u,v and z. Maybe the chain rule would be useful: $$dx = \frac{\partial x}{\partial u}du + \frac{\partial x}{\partial v}dv + \frac{\partial x}{\partial z}dz$$
etc.

3. Sep 5, 2012

### arantxa.ceped

Thank you, actually I used that one to solve the problem =)