The Principle of Least Action

Classical Mechanics and Relativity: Lecture 2 0:00 Introduction 3:18 Trajectory by integrating Newton's second law 18:21 Definition of the "Action" 24:45 Definition of the "Lagrangian" 29:34 Principle of Least Action 50:56 Euler-Lagrange equation of motion 55:52 Example: throwing a ball Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete and self-contained course in which everything is derived from scratch. In this lecture, I derive Newton's laws from a more fundamental principle: the famous "Principle of Least Action". First, we introduce and analyze the POLA, and from it derive the Euler-Lagrange equation of motion. The equivalence with Newton's second law is demonstrated explicitly. As an example application, we solve a simple mechanics problem using the new formulation. Full lecture course playlist:    • Classical Mechanics and Relativity lecture...   Course textbooks: "Classical Mechanics" by Goldstein, Safko, and Poole "Classical Mechanics" by Morin "Relativity" by Rindler