Euler–Lagrange equations have long been considered a pillar of mathematical foundations in the calculus of variations and classical mechanics. They are also often referred to as a beautiful equations derived by Euler and Lagrange. The Euler–Lagrange equations represent a set of second-order ordinary differential equations that identify stationary points of an action functional.
In other words, they allow us to optimize performance by finding the minimum or maximum value of the function on which they act. Understanding this remarkable equation is essential to breakthroughs in engineering and science applications such as robotics, aircraft design, optics, energy optimization, and much more.