Lecture 5 | Modern Physics: Classical Mechanics (Stanford)

[jayejayeee]

i enjoyed this vid

[staranjela]

love the video really good

[grisgrisy]

love the video man

[SuperDogbrown]

love the video really good

[awsomenesscaleb]

1:42:05

I think that peeve in the audience asked a question so necessary they had to cut the sound out.

[grunder20]

An instructor who knows what he's doing. Good man.

[edy141000]

a person who understands and masters physics is a great teacher, even if he is a peacful guy

[SalsaTiger83]

balancing the pendulum on the top is a standard trick for robotics

[noobyfromhell]

I think Hamilton cared for the fact that momentum is a covector, so when you differentiate something with respect to its components, indices 'flip' and you get a vector, and vice versa. So it made sense to formulate Hamiltonian mechanics with a vector and a covector: you differentiate the Hamiltonian with respect to one and get another.

[MichaelKovarik]

@noobyfromhell Well, eh, that is true with Hamiltonian dynamics. The momentum is defined to be a vector in the cotangent space of the configuration manifold (the manifold of possible spatial configurations). However, I don't think that your reasoning can be applied to Lagrangian mechanics in which the generalized velocities are simply elements of the tangent space.

[Gytax0]

What is that "feida DOT"? Why does he put the dot over the Greek letter which corresponds as an angle?

[noobyfromhell]

@Gytax0 It's theta and dot means 'derivative with respect to time'.

[Gytax0]

@noobyfromhell Thank you.

[1isaacmusic]

Anybody who eats cookies and gives lectures on physics is one cool mofo. I can't get enough of these lectures. I wish they'd arrange them all a little better and add the missing ones.

[paulojunior201]

Leonard Susskind is just unbelievable, he should be treasured lol. I love him.

[odysseus9672]

I would imagine that Hamilton's purpose was twofold. First, the canonical equations of motion tend to take the form of a system of first order ODEs instead of second order. Second, because the canonically conjugate momenta tend to be conserved quantities, the equations of motion will tend to take a more obviously simple form.

What's more, there is something of a preference for energies, or Hamiltonians, over Lagrangians which don't seem to have meaning outside of deriving equations of motion.

[TheBobathon]

Bob & Herman 26:50 :)

[thyorison]

These are great lectures and Susskind is a great teacher. It's too bad they didn't get a competent cameraman to work with him. Often the camera needlessly moves away from important equations on the board.  Nevertheless, Susskind makes these the best physics lesson I'ver ever seen, in any format.

[andrew11235]

if you knew that at time t the pendulum's energy was 0 and its theta was pi (the pendulum is stuck vertically upright), then how could you know whether it was pushed clockwise or counterclockwise to get to that position? aren't classical systems supposed to be deterministic into the past?

[andrew11235]

i guess you could say that's because it's a symmetry? anyone know?

[rahulilrplac]

Good question.. Am stuck on that too..or may be am just too stupid.

[rahulilrplac]

I think that on a y/t graph, the path of bob is given by a vertical straight line (y does not change, t does)

Since d energy is 0,its more like a ball of mass in space,with no forces on it(T n U both r 0).In such a case,the path is well just the vertical line frm - infinity to +infinity.Hence d path is deterministic.

If what u meant was dat T alone is 0,then its more like a pendulum on earth,at rest.Path again is fixed, being a vertical line on t-y.determinism is therefore given

Just my thought.

[rahulilrplac]

Also, let's say we are at angle pi.

For determinism we need to know both q and q-dot (velocity). If we know both these quantities for your setup, you will see that you can easily predict the path.

Does that answer your question?

[nathanielvirgo]

You can follow the equations back in time in that case, and you will find that it was always balanced at the top. In the case where the pendulum is swung with just enough energy to never fall down, it approaches the top asymptotically, so there's always a small displacement from the top, with a correspondingly small amount of velocity toward the top - and in that case you can work out which way (and when) it was swung. In either case determinism is intact :)

[andrew11235]

ah, of course! thanks.

[ogirv101]

This guy is really helpful, and a great teacher, I can't believe I'm watching University lectures for free.

[ethositachi]

@ogirv101

Welcome to the age of the internet where great things are possible.

[HelloIAmDaniel]

@ogirv101

Leonard Susskind truly is a man among men!

[chile1231]

Good instructor!

[mrunzi76]

lol, this guy is no ordinary physics instructor

[csmcmillion]

@mrunzi76 this guy is no ordinary physicist - he's the guy who bitch slapped Hawking.