# Equation of motion from Hamiltonian

1. Aug 17, 2015

### LagrangeEuler

1. The problem statement, all variables and given/known data
$$H=\sum^N_{i=1}(\frac{p_i^2}{2m}+\frac{1}{2}(x_{i+1}-x_i)^2+(1-\cos(2\pi x_i))$$

2. Relevant equations
Hamilton equation of motion I suppose
$\dot{q}=\frac{\partial H}{\partial p}$
$\dot{p}=-\frac{\partial H}{\partial q}$

3. The attempt at a solution
If particles are identical then
$\dot{p}=m \dot{x}$
So if I understand well I will get from here system of equations
$\dot{p_1}=-\frac{\partial H}{\partial x_1}$
If I take for example m=1, then
$\dot{x_1}=-\frac{\partial H}{\partial x_1}$
Is this correct?

2. Aug 17, 2015

### BvU

no. Check the dimensions.

3. Aug 18, 2015

### LagrangeEuler

Ok. Can I get some help?

4. Aug 18, 2015

### BvU

Yes: write down the dimensions and check,

5. Aug 18, 2015

### Jufro

In particular I think BvU is trying to draw your attention to the partial derivatives you wrote in your last statements. Check those dimensions to see if they are consistent with the definitions you wrote in the relevant equations section.