How to Solve the Euler-Lagrange Equation
Description
A detailed tutorial on the solving of the Euler-Lagrange Equation. Step by step tutorial including several examples of how to solve the Euler-Lagrange Equation for reference.
Overview
The Euler-Lagrange Equation, sometimes just called Lagrange’s Equation, is a differential equation which has a solution that is function for which a given functional is stationary. The Euler-Lagrange Equation is an equation satisfied by a function q of a real argument t which is a stationary point of the functional 
After finding q, the derivative of q, and L, which can all be expressed by seperate equations. the Euler-Lagrange Equation can be written as an ordinary differential equation expressed by
where x is typically given in radians, although it can also be a complex number. Euler’s Formula is named after Leonhard Euler, who was not the first one to discover the formula, but to put it in the form we know today.
