Classical Mechanics | Lecture 7

(November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics.

This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes.

Stanford University

Stanford Continuing Studies

Stanford University Channel on YouTube:

[joabrosenberg]

The history of Classical Mechanics and what did Lagrange look for?; Hamilton derivation of the conservation of energy 06:00; Hamiltonian describes surfaces in phase space 13:30; Flow in phase space 18:30; Divergence of the phase space flow 21:00; Liouville theorem 37:30; Expanding universe effects of Liouville theorem 53:00; Studying H=p*q 59:30; A system that doesnt conserve the volume in Phase space 1:09:00; Q&A 1:19:00; Poisson brackets 1:35:00 (Feinman sexual remark on mathematicians 1:38:30..; Susskind Equation 1:45:30...).

[liiistnen]

I never knew Mike Ehrmantraut was so good at physics

[michaelgarcia]

What I love about Suskind is his complete patience to keep asking his students for questions and his ability to continually answer one after another. Great guy and professor!

[vecter]

I could listen to this guy lecture all day.

[hasanshirazi]

Q: How Lagrangian and Hamiltonian were developed before Quantum Mechanics?
Ans: Mathematicians enjoy developing mathematical methods which seem utterly useless at the time. In fact the more useless a method seems to be, the more mathematicians cherish their discovery. When Physicists want new mathematical tools for their theories, they find that mathematicians had already done the job decades ago.
Example: When Einstein wanted to use Tensor calculus for his General Relativity, he did not have to search for it, it had already been developed by Ricci, an Italian mathematician, decades ago. Weird minds indeed!!!

[hasanshirazi]

This lecture is the heart of understanding Classical Mechanics.

[MinGWDownload]

Haven't done Hamiltonian mechanics in some time, this course brought back some memories, thanks.

[onebylandtwoifbysearunifby]

His way of visualising energy by using fluids is brilliant.

[echosystemd]

He is eating. Haha. I like his relaxed way of teaching.

[seandafny]

very great. Never dozed off not even once and very good grasp of understanding held.

[TwinDoubleHelix]

The same thing goes for an explanation of the flow under H in the phase space, that is: an intuitive understanding of what it is, how it relates conservation of whatever you like, and how chaotic systems are characterized using it. I think most textbooks do this reasonably well, but only because it is very important, and they take 50 pages to convey a worse conception than Susskind does in 30 minutes. I am yet to see another lecturer do it at all without losing the plot completely.

[gsboss]

mike has another job. but seriously, good lecture

[perjespersen]

3:50 I think that Lagrange tried to solve the brachistochrome. This naturaly makes one think of some sort of least action principle. In this problem a balance between kinetic and potential energy is also an intuitive step. Before that Euler had used the momentum as the "Lagrangian". This would be a way to be shown the door to this beatiful structure

[TwinDoubleHelix]

I am satisfied with that level of informality. Even though it is not a true statement, it is wonderfully informal.

I probably understand flows a lot better than I understand Hamiltonians. And I think I understand Hamiltonians quite well.

I get the feeling you are really itching for an argument here so let me say this (and I might speak for some of my fellow Susscult members here) : I'm not saying he is a brilliant teacher overall. I am saying he is brilliant at conveying

[bobdafoe]

One of the best lectures I've ever watched

[dqyilfx]

When the teacher calculate the momentum p for the damped harmonic oscillator, there is mistake. x^(dot) should be (p/m)*exp(-gamma*t) where gamma is the damping coefficient which is written by 'C' in the class. The Lagrangian and Hamiltonian for the damped harmonic oscillator are given in the problem 2076 in the 'Problems and Solutions on Mechanics' for major American universities Ph. D. Qualifying Questions and Solutions Edited by 'Lim Yung-kyo'.

[abhijithrambo]

Khan Academy have some great videos about vector fields and divergence. It would be really beneficial to watch them before you start this lecture.

[TwinDoubleHelix]

what is important from an intuitive point of view, with limited time and limited background/supporting information (and probably an audience with some serious limitations of their own, but that's not so important)

[custodiogomesbarcellos]

Thank you for these excellent classes. Would it be possible to add subtitles to them? Many people struggle with English and others have hearing problems. Subtitles would help a lot.

[AT-]

1:44:00 Perfect! Thank you Prof. Susskind.