where Q i and P i denote the initial position and momentum of the i -th particle. For a system of multiple particles, each one will have a phase-space trajectory that traces out an ellipse corresponding to the particle's energy. The frequency at which the ellipse is traced is given by the ω ω in the Hamiltonian, independent of any differences in energy. As a result, a region of phase space will simply rotate about the point ( q , p ) = ( 0 , 0 ) with frequency dependent on ω ω . This can be seen in the animation above.