Figure 1.

Depiction of the principle of stationary action. This figure shows that the path of least action (darker blue) is the path which is a stationary point of the action—a path for which the gradient of the action is zero. Here, the trajectory is a parabola, like the kind of path one might observe through a gravitational field. On this path, the action changes at most quadratically under the variations in yellow. Other paths in lighter blue are less ‘ideal’, in that they break the precise balance between kinetic and potential energies. That is, these paths do not move in the potential well.