Transforme kinetic energy in parabolical cyndrical coordinates

[arantxa.ceped]

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

The Attempt at a Solution

Any ideas??

 

[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.

 

[arantxa.ceped]

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