Find Lagrangian and Hamaltonian equations of motion in polar coord.

[ocan]

Homework Statement

A particle of mass m is attracted to a force center with the force center with the force of magnitude k/r² . Use plane polar coordinates and find Hamilton’s equations of motion.

Homework Equations

(L)agrangian = T-U , U=-\intF dr

The Attempt at a Solution

I can get the Hamiltonian equations of motion but what I am not confident about is the equations for kinetic and potential energy.
Are they correct?
Did I obtain the potential energy equation correctly?

Any input would be appreciated. Thank you.

http://b.imagehost.org/0511/tmp37F.jpg

 

[gabbagabbahey]

The problem tells you to use plane polar coordinates; which means it is a 2D problem and so there are two coordinates and conjugate momentums to consider. Why haven't you included any \phi and p_{\phi} terms in your Hamiltonian?