Equation of motion from Hamiltonian

[LagrangeEuler]

Homework Statement

$$H=\sum^N_{i=1}(\frac{p_i^2}{2m}+\frac{1}{2}(x_{i+1}-x_i)^2+(1-\cos(2\pi x_i))$$

Homework Equations

Hamilton equation of motion I suppose
$\dot{q}=\frac{\partial H}{\partial p}$
$\dot{p}=-\frac{\partial H}{\partial q}$[/B]

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?

 

[BvU]

no. Check the dimensions.

 

[LagrangeEuler]

Ok. Can I get some help?

 

[BvU]

Yes: write down the dimensions and check,

 

[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.