Action for the harmonic oscillator

• Unit mass is that of the oscillator.
• In the left panel you can choose the frequency ω, the starting and ending configurations (t1,x1) = (t₁,x₁) and (t2,x2) = (t₂,x₂), as well as the number of points N in the polygonal trajectory and. The trajectory points, including the end points, can be moved with the mouse.
• To get information on the other elements, put over them the mouse pointer to see the corresponding tooltip.

Activities

• Use the mouse to move around trajectory points, including end points.
• At each time the action along the current trajectory is shown in blue and, if Physical is selected, the minimal action along the physical trajectory between the two end points in red.
• You should be able to check Hamilton's principle of least action: the value of the action along the trajectories joining two configurations reaches its minimum precisely along the physical trajectory.
• The physical trajectory corresponding to the current two end points is recovered when pressing Set solution.