# Lagrangians and P-Conservation

1. Oct 19, 2006

### moonman

I have a problem with a particle experiencing a central force towards some origin, as well as a gravitational force downwards. I've calculated the Lagrangian, and the equations of motion. Now I'm being asked to see if the system follows conservation of angular momentum. How do I do this? I know it has something to do with seeing if the system is invariant of rotation, but how do I check for that?

2. Oct 19, 2006

### Euclid

If $$\frac{\partial L}{\partial q} =0$$ then the conjugate momentum $$\frac{\partial L}{\partial \dot{q}}$$ is a conserved quantity.

If that doesn't clear things up, then post what you have for the Lagrangian.

3. Oct 20, 2006

### JohanL

But the conjugate momentum is the same as the angular momentum only in some cases.
Compute H and chech if H commutes with J.