# Math Help - Hamiltonian System

1. ## Hamiltonian System

Consider a system of the form:

dx/dt=F(y)

dy/dt=G(x)

That is, dx/dt depends only on y and dy/dt depends only on x.

What is the Hamiltonian function?

2. Compute the lagrangian $L$ and then

$H = \sum^{i} p_{i}q_{i} - L$

where $p_{i} = \frac{\partial L}{\dot{q_{i}}}$ are the canonical momenta conjugated to the $q_{i}$ coordinates and $\dot{q_{i}} = \frac{d}{dt}q_{i}$

3. Do you know the physical interpretation of the Hamiltonian? We are talking about classical mechanics I guess