This is a fundamental result in Hamiltonian mechanics, governing the time evolution of functions defined on phase space. As noted above, when { f, H } = 0, f is a constant of motion of the system. In addition, in canonical coordinates (with { p i , p j } = { q i , q j } = 0 and { q i , p j } = δ δ i j ), Hamilton's equations for the time evolution of the system follow immediately from this formula.