Is a particle subject to dissipation proportional to its velocity a Hamiltonian system?

Question

Why or why not? I'm pretty sure that this isn't a Hamiltonian system because it involves a dissipation term, but using the Hamiltonian flow it gives me that the system is Hamiltonian.

Answer 1

I have a curious example :

If I take the hamiltonian $H(p,q) = (p + q)^2$, and apply Hamilton equations : I get :

$$ \dot q = \frac{\partial H}{\partial p} = 2(p + q)$$

$$ \dot p = - \frac{\partial H}{\partial q} = - 2(p + q)$$

So you have :

$$ \dot p = - \dot q$$

So it looks like very much to a dissipative system.