Figure 1.

Variations of paths under HP. By knowing the start and end points as well as the kinetic and potential energies of a particle traveling from point q(t₁) to q(t₂), we can compute possible paths that the particle may take by varying positions and momenta of the particle. The most likely path, where action is stationary, is denoted as the actual path. Here, being stationary means the derivative of the action is zero.