Principle of Least Action

I thought this video was really fun and wrote up some of the derivations that the video went over quickly. Introduction and Basic Principles Maupertuis&rsquo; principle of least action states that the action, defined as: $$ S_0 = \sum mvs $$ where $m$ is the mass, $v$ is the velocity, and $s$ is the distance, reaches a minimum along the actual path of motion. Euler later generalized this to a…