TITLE: Non-Hamiltonian actions in physics
QUESTION [5 upvotes]: I was reading the following article when I came across the interesting sentence 
"non-Hamiltonian [symplectic group] actions also occur in physics"
I took a cursory look at the article cited but nothing jumped out at me to back up the claim. Does anyone have a good example of such a thing? Ideally a classical system, if possible, as I don't have much contact with the quantum world :)

REPLY [4 votes]: The master thesis Nonholonomic Dynamical Systems by Brett Ryland contains several examples of non-Hamiltonian systems from classical physics: the dynamics of a laser and the evolution of a gas flame (page 14), the rattleback (page 29).