Classical Mechanics | Lecture 6

(November 1, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on the motion of objects. He starts with a general example of a wedge on a frictionless plane and uses it as the building block for more complicated theory.

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:

[glendeloid]

These are amazing lectures. Susskind's presentation is perfectly clear and perfectly paced, with the relaxed energy and humor of a big personality, but without the arrogance and implied intimidation that so often accompany it.

[joabrosenberg]

An example of a wedge; Second example of double pendulum 27:00; Hamiltonian and Harmonic Oscillator in Phase space 53:30; Hamilton Equations 1:13:30; Q&A 1:29:00

[ozzyfromspace]

These lectures get better and better every class!

[halilibrahimcetin]

Thanks to Leonard Susskind, I feel more confident to learn more advanced topics.

[TheMaximumGForce]

Loving this series! cant wait to get to quantum mechanics!

[seandafny]

this man is in love with harmonic oscillators.

[tobywhite]

This is fun, sort of. Susskind has a great sense of just how fast he can push without getting me totally confused and giving up. I feel like a greyhound chasing a mechanical rabbit. I never quite catch up, but I can get close enough to stay in the race if I keep running as fast as I can. (There's probably some Lagrangian to describe that kind of motion, but I don't even want to know it)

[camilodominguez]

" If you know the rules of Lagrangian Mechanics, it's a mechanical exercise, a completely mechanical exercise you can be dumb as hell and still solve the problem"- Leonard Susskind.

[roberthumphreys]

Check out his "Theoretical Minimum" series of books, available on Amazon and other booksellers! They're great, especially for people approaching the subject for the first time, or coming back having forgotten calculus!

[abhishekcherath]

I'm not getting the same expression for the kinetic energy for the double pendulum

Nvm got it


I'm amazed how well I'm understanding this. Prof is so good at explaining this stuff

[habblebabble]

Canonical momentum is essentially a definition of momentum given by the LaGarange equation. It is, by definition, the partial of the LaGarange with respect to the time derivative of the space coordinate (most recognizable as velocity). I recommend wrestling with the LeGendre transformation when you get the chance. Since the LaGarange, in general, is not always in a conservative field, the units tend to change when the cononical momentum is taken.

[EdSmiley]

Anybody who doesn't have an intuitive feeling for how complexly odd the double pendulum's equations of motion laid out by Dr. Suskind are in practice should look at a YouTube video of a double pendulum. You'll be glad you did!

[ArabyGUC]

1:20:03 Here one has to smile with satisfaction at the simplicity and elegance of the derivation :)

[jessstuart]

I think there is a sign error at 38:00. The cos(alpha) term should have a (theta_dot + alpha_dot) factor, not (theta_dot - alpha_dot).

[seandafny]

Very nice and smooth. I hope the rest go like this. Hamiltonians seem so much less complicated then them lagrangians.

[hasanshirazi]

This is a best explanation of Lagrangian and Hamiltonian.

[jamesdowns]

His explanation for how beautiful the Hamiltonian is is how you can see these phase portraits and gain an understanding of the cycles and non convergent behavior, etc... but I keep thinking to myself, "but you could take Newton's equations and just plot x vs xdot and see that too..." Also, I am slightly confused how he initially explains that it was vitally important in coming up with the Lagrangian that it must be T-U, not T+U, in order to obtain the equations of motion after applying the Euler Lagrange equation. Then Hamilton comes along and decided, "no, it's better to make it T+U" after all? Is his formulation kind of like an add-on or adjustment to the Lagrangian so that it can still give the equations of motion using the Euler Lagrange operations but also does not change with time? What does it mean, intuitively, that the action that the Lagrangian minimizes is T-U? Is it that as kinetic and potential energy trade back and forth through the course of a system in motion, that it is done so in such a way that their difference is kept as minimal as possible? Since there is no constraint on holding total energy constant with time in the Euler Lagrange, is this achieved just accidentally?

[karolispetruskevicius]

Hi all. Hope you have all enjoyed these lectures as much as I did. I was just wondering if anyone knows where I could find original lecture notes for this series? Much appreciated!!

[matschreiner]

1:29:30 - 'Quantum Mechanics would go to hell in a handbag if you tried to take some of these other cases' Haha,

[joeboxter]

+mg was right and he changed it to -mg at the urging of the same student who tried to convince him derivative sin is -cos.

If you have d/dt of momentum = -mg then you are saying the F (derivative of momentum) is acting on a falling object is not in the same direction as the acceleration. Both have to be in same direction and hence same sign.

The F is down and mg is down. So the signs on both sides have to be same. If sign is reversed then resulting Force would be in opposite direction of the mass time acceleration: g.