Advanced Classical · Module 09
Newton's approach asks what force acts at each instant. Lagrange and Hamilton ask which whole path nature chooses. The second question turns out to be the one quantum mechanics and field theory are built on.
By the end of this module
You can derive the equations of motion for any system from a single scalar function.
Why would nature 'choose' a path in advance?
Caltech
Feynman's favourite lecture. He says so himself.
Veritasium
Veritasium's treatment of least action — the framing this whole module rests on.
How do I make constraint forces vanish from the problem entirely?
Leonard Susskind, Stanford
Full free lecture course. Susskind teaches the real thing without the usual prerequisites.
Why is anything conserved at all?
Emmy Noether, 1918
The paper that explains every conservation law you have ever used.
What if I treat position and momentum as equals?
If the laws are deterministic, why can I not predict the weather?
Steven Strogatz, Cornell
Strogatz's full lecture course, free on YouTube.
Check yourself
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01The Lagrangian is:
02By Noether's theorem, invariance under time translation gives:
03In Hamiltonian mechanics, phase-space volume is conserved under time evolution. This is: