I What is the motivation for principle of stationary action

[Stavros Kiri]

I think one reason for heavy reliance on variational approaches early on was computational. In an era before computers (or even slide rules), solving equations of motion at 1000's of sequential time or space points required heroism. A variational calculation found the path all at once. Variational computations of, e.g., electromagnetic systems (and even circuits) remained popular until computers came onto the scene, as did conformal mapping and the like.

True enough. + I think they (i.e. variational methods and principles) are also related and connected to numeric computational methods even today. For that interesting connection between Variational Calculus and Numerical Methods, as well as Optimization Methods and Mathematical Programming see e.g. :

Encyclopedia of Mathematics [Variational calculus, numerical methods of]

https://www.google.gr/url?sa=t&sour...ggdMAA&usg=AFQjCNGyCnW-qeLyrtWU6zxnHOcXhfcNQg

I quote here a relevant to your comment part, (but perhaps the other way around connection) e.g.:

"The first numerical methods of the calculus of variations appeared in the work of L. Euler. However, their most rapid development took place in the mid-20th century as a result of the spread of computers and the possibility, afforded by these techniques, to solve complicated problems in technology. The development of numerical methods in variational calculus mostly concerned the theory of optimal control, which, from the aspect of practical applications, is the most important (cf. Optimal control, mathematical theory of)."

 

[Stavros Kiri]

If you seek a discussion of the principle ... than it actually does.

Acknowledged. Interesting.