Assuming you're thinking about applying Noether's theorem, you need your system to have something like a Lagrangian (or be symplectic). From a quick glance it d

Assuming you're thinking about applying Noether's theorem, you need your system to have something like a Lagrangian (or be symplectic). From a quick glance it doesn't seem to me that you can write down an action S for the system so it's not clear that you could apply the theorem to get conserved quantities corresponding to the local symmetries of S.