We consider the possibility that classical dynamical systems display motionView original: http://arxiv.org/abs/1202.2537
in their lowest energy state, forming a time analogue of crystalline spatial
order. Challenges facing that idea are identified and overcome. We display
arbitrary orbits of an angular variable as lowest-energy trajectories for
nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry
provide a natural arena for formation of time crystals. We exhibit models of
that kind, including a model with traveling density waves.