[Cleonis]

I created demonstrations with interactive diagrams.

http://cleonis.nl/physics/phys256/calculus_variations.php The following case is used as motivation for developing Calculus of Variations: the shape of a soap film stretching between two coaxial rings. (The name of the solution is 'catenoid'; a surface of revolution.) Then the discussion moves to the Catenary problem: to calculate the shape of a hanging chain. The two problems have the same solution; the curve is the hyperbolic cosine.

Demonstration of Hamilton's stationary action: http://cleonis.nl/physics/phys256/energy_position_equation.p...

The diagrams have sliders. Moving the sliders sweeps out variation of a trial trajectory. The diagram shows how the kinetic energy and the potential energy respond to sweeping out variation.