Lecture 3 | Modern Physics: Classical Mechanics (Stanford)

[@arijitgayen4674]

I'm a computer science student, but I spend my vacation mornings listening to this beautiful man. He teaches phenomenally.

[@apostolismoschopoulos1876]

Actually the same!

[@agentford_007]

same for me bro.... and i agree with you

[@SewerShorts]

@@agentford_007same brotha, this video is great

[@Sans_K5]

same for me bro coding and seeing his lectures is so much amazing

[@QuaternionEM]

Summary:
Derivation of the Principle of Least Action and the
Euler-Lagrange eq.
Derivation of Newtons laws from the PLA.
Several examples using the Lagrangian to derive
conservation laws and the associated symmetries.
Awesome.

[@meowwwww6350]

Thanks so much and after 10 years are you a physicist now?

[@apostolismoschopoulos1876]

@@meowwwww6350 What about you? After 8 months do you still study physics?

[@Xd-tl1yt]

@@apostolismoschopoulos1876 and what about you? You still study physics after 5 days?

[@apostolismoschopoulos1876]

@@Xd-tl1yt haha yes now I'm in the 5th video of the series :p

[@bingusiswatching6335]

@@apostolismoschopoulos1876 very epic

[@ruskolnikov7211]

I also love in minute 13 where he gives a brilliant intro to the functional derivative and uses Bronx words like ‘anywheres’ and ‘everywheres’ .

[@johnmcandrew9351]

Dear Prof. your lectures help me a lot through a very difficult time of my live, allowing me to recover intellectual strenght ... I'll always be grateful to you!!!

[@bendavis2234]

Same here! These lectures are therapeutic in a way

[@RedLeaderBL]

Best explanation of integration by parts I have ever seen.

[@ahmeddalile]

Exceptional Lectures!
Caution: There is a MISSING part of the Lagrangian in POLAR coordinates, just near the end of the lecture, but Prof Susskind CORRECTS it in the beginning of the next lecture (Lec. 4)

[@jordak6200]

Thank you! For a minute I thought I didn’t know calculus.

[@jreedmcu1]

I am privileged to be able to access this an my discretion, thank you Stanford!

[@Liaomiao]

I can follow the maths as i just learned calc 1-3 in my spare time, but the physical concepts are just a little too difficult for me. I feel that I only need to know a tiny bit more to understand all this fully, but right now it feels somewhat scattered. I'm still very glad these lectures are put up for all to view though. Thanks Stanford and Susskind.

[@ulalaFrugilega]

with earphones i can hear it fine ... oh, maybe by now the technical equipment is better ... feel even more lucky for being now, here, able to listen to this wonderful man, who, in the blink of an eye, makes me understand things I've been hunting for years. Ok, not hunting, but anyway: thanks soooo much to all people involved in getting this here!

[@Frostalzzz]

heh, exactly the same here. I got my engineering degree last year(after 5 long hard years) and I felt that some courses(obviously tailored to engineering studies) weren't giving us the complete picture. Most stuff we saw on quantum mechanics, langrangian, Hamiltonian, ...
were giving on a fairly superficial basis and always left me with some questions.
Now I'm following a master in Physics in my spare time while working as an analog design engineer.

[@yigithanmehmetkose8777]

Can i contact you in some way? I got loooot of questions because i am in the same path!

[@Robin90modell]

These are intended as introductory physics courses, but some calculus course would probably be beneficial.
It's also intended for people who haven't done mathemathics for a while, so having a repetition of integration by parts is probably not to bad.
They go at a slow pace, probably because the intention is that you should be able to follow them with no or little time spent trying to solve problem related to the material.

[@tetraphobie]

1:30:53 I think Leonard forgot a second term here (mr(θ′)^2) aka the centrifugal force. In the next lecture he revisits the problem and writes the correct formula. So please don't be scared if you've noticed and keep watching. 😅 (Also, good job paying attention, everyone who noticed!)

[@oniyaajila]

Symmetry with respect to the x-axis in a plane means that if you replace y with (-y), the equation still means the same thing. For example, the equation x=y^2 is symmetric with respect to the x-axis because (-y)^2=y^2.

[@vaibhavgupta951]

I wish I had a teacher like you sir. Feel so lucky to be able to listen to these wonderful lectures. Thanks a lot.

[@Akhin]

I feel so grateful for having access to this

[@robertwilsoniii2048]

The interval of a derivative explanation was really well explained, clear and understandable.

[@ripperduck]

These lectures are FAR better than any physics lecture I ever had at U of O

[@fielsjd]

I feel so privileged to have access to these lectures. Thanks, Stanford.

[@marsCubed]

I loved uni, I could happily sit through physicslectures all day to nourish my mind.
Thanks Stanford.

[@jessicasfakeaccount]

click here: 1:13:40 to watch leonard susskind use abstract theoretical physics to demonstrate conservation of momentum, under the assumption that the earth is flat.

[@jessicasfakeaccount]

listen....
it'd be fine if this was an introduction to newtonian mechanics in a grade 12 class. but, he just spent three hours building up an extremely abstract meta theory, to throw it all away in a bunch of backwards assumptions that should not be made in the context of doing this in such an abstract way.
the earth is not flat, and dU/dx is consequently not zero.

[@jessicasfakeaccount]

yes, this is a course in classical mechanics. and, yes, that's a simplifying assumption that is just fine in the context of classical mechanics. but, wasn't the point of building up the theory he just built up to work through those assumptions more rigorously? why bother if you're just going to make naive newtonian errors?

[@jessicasfakeaccount]

there should be a limiting process, there - and, yes, you're going to end up with zero in the limit in the end. but i came here to see that done.

[@jessicasfakeaccount]

for now, i'm just going to ignore this catastrophe and otherwise let him finish.

[@elosant2061]

I don't see this as a particularly grave error in pedagogy here, this was just a simple example to illustrate how one would approach a classical situation in this way. He made clear his assumptions at the start, namely that we are considering particles near the surface of the earth (whereby we can use the approximation that the earth is a plane as you say, and that the gravitational potential takes a form linear in height). We would still have translational invariance if we were to consider a larger case. Rigour is missing throughout this entire lecture in much more important ways (in particular: forgoing the definition of generalized coordinates, handwavy motivations/definitions about the action, lagrangian and so forth), to the extent that I wonder why you are concerned with the most reasonable simplification. By your own logic one could argue that the newtonian approach is itself naive and we should start considering GR. I understand your perspective, indeed I am studying pure mathematics (at least independently for now until I start going to university in October) and in my time learning physics I have noticed quite a stark lack of rigour in the physicists approach compared to the mathematician's one, but in my view this particular reservation is unwarranted.

[@NoTryOnlyDo]

Excellent lectures, really helping me with my Calculus of Variations Module... Thankyou Stanford and Leonard Susskind!

[@RalphDratman]

He has explained integration by parts to this class! I love it.

[@yashwantsarav2433]

Superb lectures! Thank you Stanford.

[@doublebitaxe]

@rmnbrw Technically the "Dirac delta function" is not a function, though it can often be thought of as a function. In this case I don't think the dirac delta should be considered; however any arbitrarily tall and skinny spike would be ok. In this context, the "blip function" needs to have some width.

[@bartholomeosphinx4382]

1:05:40 -- He is not differentiating correctly by the variable x_2

[@grunder20]

Physics deals in everyday life. From the moment you wake up, until the time you go to bed. Great video!

[@chrisfreude7993]

I am not sure how dL/dalpha is derived at 33:25 - is this just the chain rule or am I missing something?

[@special-delivery]

Yes it is just the chain rule but for the multivariable case.
For f(x,y), the rule is df/dt = ∂f/∂x * dx/dt + ∂f/∂y * dy/dt
Now, for ℒ(q,q'), the rule gives ∂ℒ/da = ∂ℒ/dq * dq/da + ∂ℒ/dq' * dq'/da
where he directly substituted dq/da = f(t) and dq'/da = f'(t).

[@edlynnnau536]

Can hardly hear with volume all the way
up!

[@SUONIndustry]

thank you very much Stanford University.

[@meowwwww6350]

Oh hi Mr bear grylls

I believe that theres is a error on the derivative of lagrangian in the minute 1:31. Thank you VERY MUCH for this lectrues.

[@parallel041]

if everything can drive from energy..we can forget force?

[@KipIngram]

I love these lectures. The one down side, though, through SO MANY of Susskind's lecture courses, is that one guy in the audience who, far above and beyond anyone else, just WILL NOT stop butting in. Questions are great, but there comes a point where you just need to learn to SHUT YOUR YAP.

[@cristinaradulescu-banu3502]

Some of those comments from the guy in the audience are pretty insightful

[@munawarkarim8026]

Newton's laws are limited to objects with mass. Dealing with fields which have no mass is beyond Newtonian laws. However, the Lagrangian or Hamiltonian approach where we deal with energy, is the only approach. Textbook examples asking for solutions describing beads sliding down wires don't do justice to the Lagrangian/Hamiltonian approach. More such examples should be included in textbooks.

[@marcindotcom]

Fantastyczne wykłady, niesamowita wiedza!

[@AlexRamek]

This is because we are given a set of {q_i} and {f_i}. The only thing we vary is alpha. when alpha is zero we have the "true" trajectory.

[@PeagmaticDreamer1199]

Amazing lectures, Thanks Prof. susskind!

[@LaureanoLuna]

So. finally, the fact that the derivative of A wrt alpha is 0 at alpha=0 is not used. The fact relied upon is the more general fact that the derivative of A wrt alpha is 0. Or am I wrong?

[@BArdekani]

There is a problem with Professor Susskind's derivation. Please see here for a concise derivation that does not involve alpha. mathworld.wolfram.com/Euler-LagrangeDifferentialEquation.html
The second method in this link is akin to Professor Susskind's derivation but involves a little more complicated derivation than what is presented in the lecture.

[@LaureanoLuna]

Babak Ardekani Thank you very much!

[@marcobaioletti3777]

The fact is A'(alpha)=0 when alpha=0 is crucial, prof. Susskind uses it but he doesn't say in an explicit way (or at least I didn't notice). Indeed the derivation of Euler-Lagrange equation is done by computing the derivative of A(alpha) with respect to alpha and then setting alpha to 0. If you don't set alpha=0 the equations should be written in terms of q(t)+alpha f(t) and q dot(t)+alpha f dot(t), instead of q(t) and q dot (t).

[@SalsaTiger83]

I like the attitude, normally integration by parts would be considered part of the "most basic mathematical foundations obvious to the most casual observer"

[@Mouse-qm8wn]

Can somebody please tell me which level this lecture is? Batchelor or college?

[@jreedmcu1]

I am privileged to be able to access this an my discretion, thank you Stanford! but i do have a hard time hearing.

[@TurtleTube123]

a little mistake in the equation he writes from 1:31:00 i think, m r double dot is not minus partial U to r because it's actually partial L to r and L depends on r not only through U but also through the kinetic term of the angle.... (it's the centrifugal term)

[@ruskolnikov7211]

My high school calc teacher could’ve saved us some grief by showing us minute 3:11 to 5:20

[@bingusiswatching6335]

I just wanted a good explanation for poisson brackets but these lectures are just so damn good

[@AdityaKumar-ph4gg]

why does dL/dalpha = 0 for all fi?

[@АлексейСалихов-з4ч]

The polar coordinates part seems to be incorrect. Radial component of momentum can't be m(d^2r/dt^2). If we assume U(r) = 0 and d(theta)/dt =/= 0, then linear momentum is not conserved.

[@nacho74]

d/dt mr^2 theta• is zero

[@nacho74]

so it remains the same

[@andreaspedersen2228]

at 23.40: I can see that A becomes a function of alpha, but why not also a function of q and f?

[@ijcurtis]

I believe we are only interested in seeing the effect on the action by increasing alpha. We take q and f to be given functions. We could write something like A(alpha; q, f).

[@edyt4125]

21:00

[@ant3978]

i cant quite see why dA/d(alpha) must be equal to zero, i know the action must be minimum but i cant see where alpha fits into it

[@ant3978]

nevermind i get it the action is a function of alpha

[@jellyfish501]

Tnx Stanford ofr this videos. I really enjoy seeing and hearing this.
Susskind really gives a best view of the basic principles in physics, and science
And puts down the basic assamptions on the table as should be
Thank u mister really inspiring and helpfull

[@kmav81]

integral A(t)f(t) = 0 only implies A = 0 if A is continuous?

[@DaveJohnsonsuvam]

thats one of the major problems (slow) but you can always download it and play at 1.5x speed

[@lucianoosinaga2980]

in the last example, Did he forgot to include the part of the partial derivative of the Lagrangian with respect to r depending on the kinetic energy given by the speed of rotation (mr•theta²? or am I missibg something?

[@nacho74]

you mean the momentum conjugate of q :
m*r^2*ø•

[@tetraphobie]

Very late comment but in case anyone else was wondering, I also think a term is missing! In the next lecture he revisits the example and writes the correct equation.

[@kavitabani6340]

This is just wow

[@domasvaitmonas8814]

Would it be true to say that if the translation symmetry was not assumed in the example, then Newton's 3rd law would not be correct? I mean, if we take that potential energy is a function of both coordinates for example: U=U(x1,x2), then the derivative of dU/dx1 is not equal to -dU/dx2 and so dp1/dt = -dU/dx1 and dp2/dt = -dU/dx2. But then again, I suppose U=U(x1,x2) would mean that these two particles do not interact. Am I right or am i missing something? Thanks for the videos, this is soooo awesome.

[@nacho74]

Domas Vaitmonas well, the derivative is equal to the opposite

[@faroukmokhtar6900]

I think there can be in principle an interaction that is U(x1,x2) and then the 2 forces won't be equal and opposite.
However, since newton's third law is an observed law of nature, we don't observe such a weird interaction.
We can further turn the thinking around and say: translational symmetry in nature implies that forces be equal and opposite (raising the fact of symmetry from an assumption to an axiom)

[@Sans_K5]

thanks_Sir🙏❤️

[@TheOvermaster]

@ibreakkidslegs he explains it slowly - but this is in no way basic classical mechanics...

[@aditya-ps1cd]

prof. susskind did a mistake in lagrange equation of motion in polar coordinates:
del(L)/del(r) = m.r.(d(theta)/dt)^2 - del(U)/del(r)

[@enaud847876]

what mean for del?

[@enaud847876]

you are right.. it's an error?

[@tyskstil]

Agree. Now, what does that imply for his conclusion regarding conservation of angular momentum?

[@grandpaobvious]

You don't differentiate L w.r.t. r, you differentiate L w.r.t. r dot.

[@ajaatshatru8665]

actually L is differentiated w.r.t r dot on LHS and w.r.t r on RHS so there is a mistake. And that's the centripetel force term. mr(theta dot)^2= mv^2/r

[@pedrofonini]

I think what matters is that the integral of A(t)dt is zero

[@FoolHarvey]

...this is not an undergraduate class...the people in this class have paid money to be in the company of an emminent physicist. I think the lectures are great...I have a degree in electrical engineering though...whats your background ?

[@patriciaheil6811]

Sadly these last two videos aren't useful because the audio is so soft. The captioning helps but WTF is an "ethical czar" in physics?

[@andrewlace55]

I miss going to Stanford, wonderful school.

[@wideeyedraven15]

Or you should be flogged for being so safely rude in the anonymity of the Internet. Troll. This kind of presentation, given for free, is gold. The sound could be louder but I can hear it. Your ingratitude and lack of manners is disgusting.

[@wdrun1993]

that is sad, the view count should be higher. thanks Stanford

[@MyAce81]

@yes1123 Ah, yes, sorry, you are correct. Or at least i see the problem now. That term would correspond to some "pseudo-force" i guess? The centrifugal force maybe?

[@rmnbrw]

well f(t) is ANY function, so it can be infinit at 0, as for example delta function and have integral of 1 with your defined A(t)

[@alfonsas35]

people must see the dynamics of problem solving, powerpoint is not good for that

[@FarFromEquilibrium]

why is lecture 2 private??

[@AntonioMartinez-fv1vt]

susskind be smoking that fire!!!!

[@MyAce81]

@yes1123 He doesn't say that. First of all, they are two separate equations he writes down on separate lines (the lower equation is the time derivative of the upper one). Second, the reason that the term you mention doesn't come into account is that the derivative is with respect to r-dot (not r, look close), and the second term of L does not explicitly depend on r-dot.

[@MindXtube]

@fielsjd All education should be free.

[@meowwwww6350]

Yea

[@bingusiswatching6335]

How would teachers make money then, if it was free much less people would become teachers and we'd have even worse of an education issue ironically

[@takebackkean]

i know right they charge people 20k for this.

[@Bhuji]

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[@superok4luv2u]

isn't this hamilton principal not principal of least action

[@Bhuji]

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[@billysmith3070]

"any wheres" lol

[@jlpl3291]

I don't get the president of China joke...?

[@ixypeng7820]

In year 2008, the president of China is HU Jintao, in which HU sounds like "Who". Therefore, HU (who) is the president of China.

[@deathtokoalasstub]

@@ixypeng7820 during this period, the premier's name was _when_ which, as robert newman pointed out in _a history of oil_ , is a perfect set-up for a demented vaudeville routine, which this lecture bizarrely gets halfways to.

[@bartholomeosphinx4382]

who is that obnoxious guy who keeps coughing into the mic

[@tomaszdzieduszynski]

26:00 Omg, he got me scared! :o

[@awsomenesscaleb]

Did that guy seriously just get offended because the professor called curved coordinates screwball? WTF.

[@ankitbhankhur]

jokes at 00:43:48, 01:14:23

[@H4zarD1337]

720p pls :D

[@jessicasfakeaccount]

if you're keeping track, though, we've learned watching these lectures that susskind is both a conspiracy theorist and a flat-earther.

[@emiliosani9924]

you must be a new Einstein...

[@jessicasfakeaccount]

@@emiliosani9924 i'd rather be beethoven than einstein.

[@pphilosophy2156]

How could he possibly be a flat-earther? Give me the time stamp for that one. :o

[@edyt4125]

56:00

[@edyt4125]

22:00