The Euler-Lagrange Equation

The Euler-Lagrange equation is a mathematical tool that allows us to find functions which minimize certain quantities, such as a path function that minimizes the energy in a system or the distance between two points. This equation is foundational to variational calculus and simplifies many problems arising in physics and engineering. In this poster we will do a simple derivation of the equation before demonstrating its utility in solving physics problems using Lagrangian mechanics.