Classical Mechanics | Lecture 5
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- เผยแพร่เมื่อ 24 ส.ค. 2024
- (October 24, 2011) Leonard Susskind discusses different particle transformations as well as how to represent and analyze them using tools like the LaGrangian.
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
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Stanford University Channel on TH-cam:
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A rehearsal and expansion on the exact definition of symmetry; rehearsing conservation laws 29:00; Energy conservation 50:00; Hamiltonian and examples 1:17:00; Q&A 1:27:00; rehearsal and summary 1:30:00; Q&A 1:36:00; An example for non standard Lagrangian 1:50:00 ;
When you see delta, think epsilon, an infinitesimally small quantity. You're welcome.
These lectures are wonderful and make me wish I was at Stanford instead of McDonalds. On a brighter note, Professor Susskind is the most intuitive classical physics lecturer I have ever come across, and being able to experience his presentations is a blessing I'm very grateful for.
Best wishes, and thank you for making this content openly available +Stanford University.
Yours,
Float Circuit.
Float Circuit I feel the same way, his way of presenting things is very intuitive
if mike from breaking bad taught you physics, instead of stuffing you in a barrel
student in classical mechanics: why
teacher: quantum mechanics
student in quantum mechanics: why
teacher: no idea
nice user name
they will say quantum field theory, won't they?
A summary of everything from lesson 1 until now about principle of stationary action, lagrangian, conservation, symmetry and Hamiltonian at 1:35:35
Universe thanks!
This guy is the best lecturer ever!
1:56:00 I think we can include friction in Euler-Lagrange equation. It doesn't included in Lagrangian but in the Euler-Lagrange equation as, dL/dq + F_fric = d/dt (dl/d(dotq)) instead of dL/dq = d/dt (dl/dq-dot). Source: Problem 7.12 in John Taylor's classical mechanics textbook.
It is very exciting how by his answers LS extrapolates ~Ok questions from the students to become interesting questions :)
Man im jus finna restart watching dese at from da first lecture
I used mathematica to solve the equation he made up at 1:57. With the initial conditrions that I chose it is a parabola. I used mathematicas "VariationalMethods" and applied the EulerEquations function, using x instead of q and with initial conditions x[5]==1, x'[0]==1.
The lines of code follow.
0},{x[t]->-Sqrt[E^(2 C[1])-t^2-2 t C[2]-C[2]^2]},{x[t]->Sqrt[E^(2 C[1])-t^2-2 t C[2]-C[2]^2]}}
equationOfMotion = DSolveValue[{DifferentialEquation, x[5] == 1, x'[0] == 1}, x[t], t]
Note the above has initial conditioons to give a specific solution,
Sqrt[76-10 Sqrt[51]-10 t+2 Sqrt[51] t-t^2] Note this is the specific solution.
So it is in fact a perfectly valuable trajectory.
No disrespect intended for the creators of this wonderful series of videos.
At 1:42:25, he mentions how the question under discussion is really common.
This I think, is why:
In my QM classes, they would say to us "Hey! Do you remember that Lagrangian from classical mechanics? Well in QM you use it the same way!". In other words, use of the Lagrangian in QM is motivated by what we learned in *classical mechanics*, not the other way around!
So we're stuck in this situation asking ourselves "Why is the Lagrangian so fundamental? Isn't it just a weird trick that produces Newton's equations? Why does that work?" and apparently, according to Mr Susskind, the answer to this doesn't lie in classical mechanics.
Similar structures are used in machine learning algorithms (especially regression). For me the "cost function" used in machine learning is always like some kind of Lagrangian without potential energy part.
+Öncü Kayalar
The Lagrangian without the potential energy is the case with most non-mechanical systems. The derivation of the Euler-Lagrange equations makes the assumption that potential energy is independent of velocity after all.
Anand, the explicit derivation of the EL equation doesn't place the restriction you mentioned on the potential energy function. For clarity, check out the short derivation th-cam.com/video/sFqp2lCEvwM/w-d-xo.html by the TH-cam channel Faculty of Khan (this was my first look at variational calculus).
I hope this helps.
Robin Wilson well in quantum mechanics there is the path integral formalism where the probability to find a particle somewhere is a sum over all possible paths it could've taken to get there. Each path contributes a a number that depends on the action of the path. There is a limit where the path integral formalism results in the principle of minimum action in classical mechanics
awe shit. Finally gaining a somewhat firm understanding. 👆
Time translation having concept similarity to Entropy.
The Entropy of a process/system may decrease or increase, but Entropy of the Universe(system+surrounding)/Isolated system/Cycle always 'Increases'
How does we decide that a conserved quantity should be formed a certain way? In other words, how do we know it should be the product of two terms in this particular example?
@1:30:38 Good summary.
all equations used in this and last lecture on whiteboard - 1:35:43
thanks sir for these amazing lectures❤🙏
While obtaining the Hamiltonian formulation, there was the sum over Pi d qi /dt. It would make sense to say that it is the sum over all the coordinates. However, is it necessary that the Hamiltonian should include all the particles, i.e, is that sum encompassing all particles?
lecture starts at 9:05
Important point at 24:15
He is very patient with his students who interrupt him very often !!!
At 53:40, I thought of radioactive decay. In terms of time invariance, I guess we have half life (and energy if we include all mass/energy in the nucleus before the decay), among other possible things. On the other hand you could say that the experiment is "sensitive to delta t" as Dr. Susskind says, if you just take whatever is contained in the nucleus as the system. This is why we can do radiometric dating. Doing the same exact radiometric dating experiment 1000 years ago with carbon isotopes is clearly a different experiment, if you assume all the same initial conditions as you would 1000 years later. Just wondering if I'm on the right track here in how I'm thinking about this. Feedback is appreciated, although I understand the last comment reads as being posted one year ago lol.
By the way, somebody tell genius Susskind that Goldstein was neither engineer nor chemist.
"Herbert Goldstein (June 26, 1922 - January 12, 2005) was an American physicist and the author of the standard graduate textbook Classical Mechanics [...]
He received a B.S. from City College of New York in 1940 and a Ph.D. from Massachusetts Institute of Technology in 1943.
From 1942 to 1946, Goldstein was a staff member of the wartime Radiation Laboratory at M.I.T., where he engaged in research on the theory of waveguides and magnetrons and on the characteristics of radar echoes. He was an instructor in the Physics Department at Harvard University from 1946 to 1949. In 1949-50 he was an AEC postdoctoral Fellow at M.I.T., and served as a Visiting Associate Professor of Physics at Brandeis University, 1952-53. From 1950, Goldstein was a Senior Physicist at Nuclear Development Corporation of America, where he directed theoretical research on the shielding of nuclear reactors and on neutron cross sections of interest for reactor design.
From 1961 Goldstein was a professor of nuclear science and engineering at Columbia University. At the time of his death he was professor emeritus.
Goldstein won the Ernest Orlando Lawrence Award in 1962 for his "contributions to reactor physics and to nuclear cross sections, and for his leadership in establishing a rational scientific basis for nuclear shield design".
He was a founding member and served as president of the Association of Orthodox Jewish Scientists. He was buried in Israel."
Quote from a website known as Wikipedia.
at 1:51:13 Maybe he meant to say "the Lagrangian does not look like a conventional Kinetic minus Potential energy but you still need to perform T-V to get the Lagrangian" , rather than say "the Lagrangian does not lend itself to a conventional kinetic minus potential energy" ? Or maybe we arrive at Lagrangian by not only performing T-V but can also do it through a process like his derivation?
OOps I solved the first equation he put up, the one with the q times q dot at the end. He then erased these term before proceeding. Here are the corrected inputs.
0},{x[t]->-Sqrt[E^(2 C[1])-t^2-2 t C[2]-C[2]^2]},{x[t]->Sqrt[E^(2 C[1])-t^2-2 t C[2]-C[2]^2]}}
Repeat with initial conditions
equationOfMotion = DSolveValue[{DifferentialEquation, x[5] == 1, x'[0] == 1}, x[t], t]
specific solution
Sqrt[76-10 Sqrt[51]-10 t+2 Sqrt[51] t-t^2]
at 1:46:25 a student asks how do you know when you can not use T-V. I think perhaps when the system you are using is non-equilibrium, as would be the case if your system was exhibiting friction, and friction was not modeled in your total kinetic and potential energies?
34:57 how ?
I think I know why he is going through the long derivation of Lagrangian for simple systems... because more complicated systems later will require similar derivations to find the Lagrangian because we do not necessarily know what the Kinetic and Potential energies are. Anybody care to confirm , or correct, or add to my comment?
0:50 I think it's David Morin's "Introduction to Classical Mechanics". Griffiths made a (beautiful) electrodynamics book, and a book on QM (less beautiful unfortunately...)
what level of physics is this? I don’t recall seeing the Hamiltonian in Honors Physics at Cornell
anyone know where to find Dr. Susskind's notes directly?
***** You can download them here
libgen.net/view.php?id=1018385
It's an illegal Russian web with millions of books
that's awsome,pretty much anybook you want,from science to mathematics
Leonard Susskind published an excellent book called "The theoretical minimum". It has the same material as these videos and was very useful for me.
Juan Garcia 5
Juan Garcia was
Thank You !
i am dumb as the chair i am sitting on, and if he can make me understand, he can make pretty much anyone understand it.
I don't understand what they're talking about at the start of the video
1:56:28
This lecture series are awesome. And bugüne kadar niyesini anlamadığım şeylerin cevabını bulabiliyorum. Mükemmel...
aynen, kitapları daha iyi ama, çok güzel örnekler var onlara da bakabilirsin :)
did he just casually use gravitational wave as an example for a time-dependent lagrangian...??? 1:06:32
Afaik there is controversy about whether they obey energy conservation so that doesn't seem surprising
What does the curly L versus not curly L signify? Like why does he correct himself to make the curly L straight L sometimes but not others? What's the difference?
I think there is no real difference. Maybe he does not want to confuse the audience. On the other hand maybe he is just randomly discussing it as a point that happens to be interesting to him for some reason.
Straight L IS the Lagrangian, and he wants to be using that. The curly L is the Lagrangian density which is used in field theory where the principle of stationary action involves an integral of the Lagrangian *density* over time and also over all space, dtdxdydz. Advanced field theory physics works with the Lagrange density, and that is what he is usually working with, so he forgets to write straight L.
A rockstar of eras and 120k views, while kondizilla (don't even ask) has millions views per video, that is why we are not getting much further from our fellows chimps.
I don't understand how he seems to have proven the conservation of energy. I thought it was something that couldn't be proven.
Chandu S He showed that the derivative of the Hamiltionian is 0 if the Lagrangiaan is not dependant on time, so from that it follows that H is conserved.
Chandu S Certainly can be proven - that's a basic part of physics.
Noether's theorem.
What he is proved is that symmetry in translation of time is equivalent to conservation of energy , of course given the principle of least action.
Lol.. they drove him crazy at the end. wtf! which came first? energy or Lagrangian. I would say lagrangian or hamiltonians were put together much much earlier before they start calling them "energies" or stuff.
👏👏👏
Can we see the notes?
"A capacitor is just two metal plates", obviously not an electrical engineer.
Goldstein was not a chemical engineering LOL !
1:10:00 My goodness that is the ugliest sigma I have ever seen! Amazing lectures though.
Argh why does he have to eat, makes it difficult to hear questions.
Somebody tell genius Susskind that talking while eating is impolite and disrespectful and makes disgusting noises nobody wants to hear. i mean, seriously?
+NeedsEvidence He is doing this for free, sharing knowledge that only trained theoretical physicists know and giving it to the general public. I think he can atleast have a snack after explaining something for 2 hours.
+darkdevil905 Since when is doing it for free (which I'm well aware of) an excuse for bad manners? If he wants a snack, have a 5 min break.
NeedsEvidence I can see that being a problem of manners, but different manners exist for different places and for different people. If people in the classroom don't mind and if it doesn't disturb the overall performance of giving information to everyone evolved, then it is really not a problem. I do also agree that it is not particularly polite in general, but in my perspective it is really not an issue, if it disturbes you then it's a shame, but you can't really complain, you're learning classical mechanics without having to pay for anything except for internet reception unless you are in a public access network like a library or something.
+darkdevil905 I might be sensitive on this issue, but imagine a lecturer would burp or fart repeatedly. Not all students would shrug this off by saying "hey, it's free and I'm learning". I also don't think that all people in the classroom are OK with Susskind's eating habits. And Susskind knows he's being recorded and watched by a much wider audience all over the world. Almost universally eating while talking is considered rude. But Susskind is doing this in almost in all Theoretical Minimum lectures.
As a physicist myself (interested in the didactic pf physics, the reason I watch the videos) I've attended many brown bag seminars. Never ever have I witnessed a lecturer smacking over cookies, especially when having a mic close to his/her throat. Unthinkable.
NeedsEvidence You're absolutely right, sorry about that. Funny you mentioned you were a physicist i'm almost finishing my undergrad degree in physics, he should not be eating in front of his class, but i must say his lectures are really useful even for someone who needs to go over some topics in physics.
1:41:14