# Find Lagrangian and Hamaltonian equations of motion in polar coord.

1. Sep 22, 2008

### ocan

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

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.

2. Relevant equations

(L)agrangian = T-U , U=-$$\int$$F dr

3. 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 [Broken]

Last edited by a moderator: May 3, 2017
2. Sep 22, 2008

### 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?