Euler-Lagrange Equation

The Euler-Lagrange equation is the cornerstone of 2024-01-23 Lagrangian Mechanics. It is given by

$$\frac{d}{dt}\frac{\partial L}{\partial \dot{x}}-\frac{\partial L}{\partial x}=0$$

Where $L$ represents the Lagrangian and the arbitrary variable on the bottom can be any variable of motion within the system of coordinates you are working in, including Cartesian Coordinates, Polar Coordinates, Cylindrical Coordinates or Spherical Coordinates