Lagrangian Mechanics

Newton was a genius, able to describe the motion of objects in terms of forces and accelerations through his laws of motion. However, his laws are not always the most convenient way to describe the motion of objects.

Throughout history, there were many alternative formulations of classical mechanics. One of the most famous is the Lagrangian formulation, which is based on the principle of least action.

In this mini-series, we explore the principle of least action, the Lagrangian, and use them to derive the Euler-Lagrange equations, which are the equations of motion in the Lagrangian formulation. We apply these equations to simple systems, such as a particle in a gravitational field and a double pendulum, to see how they simplify the problem of finding the equations of motion. Finally, we explore some more advanced topics, such as Noether's theorem.