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 le...  

Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler