Richard Feynman's path integral explanation of quantum mechanics basically generalises this principle, applying it to the calculation of quantum mechanical wavefunctions.
Naturally, calculus of variations goes beyond classical mechanics, and the Euler-Lagrange equation can also be use as a mathematical analogy to solve similar problems. Consider the following question:

6.2.1 A surface of revolution has two rings of radii r1 and r2 as its boundaries at a1 and a2 along a straight line. What should the shape of the surface be such that it has minimum area?

We note that the surface area, A can be found by setting up the following equation: