Consider any trajectory q ( t ) (bold on the diagram) that satisfies the system's laws of motion. That is, the action S governing this system is stationary on this trajectory, i.e. does not change under any local variation of the trajectory. In particular it would not change under a variation that applies the symmetry flow φ φ on a time segment [ t 0, t 1 ] and is motionless outside that segment. To keep the trajectory continuous, we use "buffering" periods of small time τ τ to transition between the segments gradually.