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’ 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 continuous form:
