# 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.

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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.

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