[Cleonis]

About Hamilton's stationary action (which you refer to as 'least action').

I have created an educational resource in which I address the question of how it comes about that F=ma can be recovered from Hamilton's stationary action. This resource gives a two-pronged approach: the concepts are illustrated with interactive diagrams, and parallel to that a full presentation of the mathematics.

I start with a discussion of the nature of Calculus of Variations. I use the problem of a soap film stretching between two parallel concentric rings as motivating example. This leads to a derivation of the Euler-Lagrange equation.

Then I move to the Catenary problem. Interestingly, with the catenary problem both approaches are possible; you can solve for the catenary with differential calculus (as Leibniz did) or you can apply calculus of variations. What that means is that the catenary problem can serve as a Rosetta stone, offering a bridge between differential calculus and calculus of variations.

http://cleonis.nl/physics/phys256/calculus_variations.php

The discussion specifically for Hamilton's stationary action is in an article of its own:

http://cleonis.nl/physics/phys256/energy_position_equation.p...