Q:

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

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.

A:

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.

