Conservation laws and Noether's theorem

Classical Mechanics and Relativity: Lecture 8

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 discuss conservation laws within the Lagrangian formulation of classical mechanics. I show why certain physical quantities are conserved (do not change with time), and the conditions for which this arises. In the second part I introduce Noether's theorem, which makes the deep connection between continuous symmetries and conservation laws. We will see explicitly how translational invariance is responsible for conserved linear momentum, while rotational symmetry implies conservation of angular momentum.

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