# Transforme kinetic energy in parabolical cyndrical coordinates

## Homework Statement

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

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

## Homework Equations

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

Any ideas??

## Answers and Replies

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.

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