To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

Hi Eugene, I've got a question! At 14:43, ∂L/∂ẋ changes in time such that both points go 'down' the Langrangian -- but what if the slopes of ∂L/∂ẋ at time 1 and time 2 are such that both points go up? In that case, would an increase in action result? In other words, why is d/dt(∂L/∂ẋ) considered the DECREASE in action -- in some cases couldn't it also be an increase? Thanks!!

Khutoryansky teaching philosophy: You never really learn something until you make a full-color computer graphics animation of it set to classical music.

Me: Some cool animations, pretty colors, seems easy enough to follow along--- Video: We have to take the partial derivative of the Lagrangian with respect to x dot. Me: aw hell.

Important News: I will soon be enabling a KZfaq feature which allows people to add subtitles in foreign languages. It will also allow people to add translations for the title of the video. Each person who views the video will then have the option to select which language they want to see. The people helping with the translation enter the text, but not the time when it appears. I want to set the timing myself, so as to minimize the interference with the animation and the English text that is already a part of the video itself. I am still in the process of setting these timings. I already have several videos ready for receiving translations. These videos are the ones with the “cc” underneath their thumbnails on my KZfaq home page (“home” tab or “videos” tab.) Please check back periodically to see how which other videos now also have the “cc.” In addition to adding translations, people will be needed to help check and verify the translations that have been submitted. Details about all this are available at support.google.com/youtube/answer/6054623?hl=en

The KZfaq feature for allowing people to add subtitles in other languages is now enabled for all the videos on my channel. To add a translation for this video, click on the following link: kzfaq.info_video?ref=share&v=EceVJJGAFFI There is a similar message now pinned at the top of the comment section of each of my videos. When you are done providing the translation, please remember to hit the submit buttons for both the video subtitles and for the video title, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

From my first years as an undergrad, to me now pursuing my MSc, you have always been there when I needed you the most. Thank you Eugene Khutoryansky.

As someone who already understands Lagrangian mechanics (at least somewhat), I was able to follow this video just fine. However, I feel like for the uninitiated, some of the visuals could be a bit obtuse to understand. In particular, using balls for the curves made it difficult to see clearly what the slope is cleanly at times. Also, when you have a clock follow the path, you often have it pointed in a direction so that the face cannot be seen. I think that the clock is not really necessary anyway, because you draw the path out over some period of time. I also think that it would have been good to show the changes to the Lagrangian together. At 14:00, you show them individually at the same time, but then you show only two of the three points that are changing immediately afterwards, and I think it would’ve really made it pop if you showed that wiggling the ball in the middle back and forth in the x direction makes the neighboring balls move in opposite directions in the x^dot direction.

Thanks for putting effort in educating people, here is my comment.

this video was for those who already had an understanding about Lagrangian..

I sincerely wish to thank you Eugene for this thoughtful and inspiring video visualization lecture. It is right on time.

If you like this video, you can help more people find it in their KZfaq search engine by clicking the like button, and writing a comment. Thanks.

As someone who loves learning physics but isn't pursuing a career in it, it's such a gift to gain insight like this into our understanding of nature. Thank you very much!

I want more on this, hopefully even easier and with more specific examples. While you explain this very well, it still goes over my head at times, not just the math but what is "action" or how does this applies to a simplified-yet-realistic "vibration" (particle or whatever) in the physical world. Loving it anyhow, as always.

For a long time I've had trouble understanding why the principle of least action is often taken as axiomatic and fundamental and physics is more or less based on it. You description of the "principle of static action" really helped. Awesome videos!

Mr. Khutoryansky you are a prince among men. Thank you so much for educateing the masses. Your tutorials are all so very well illustrated. I especially appreciate the video on metric tensors. Please continue the good work and I will be making a donation to your efforts shortly.

Personaly, that's your hardest video to understand up to now.

Such beautiful explanatory animations, and even though I cannot understand all the topics I appreciate them nevertheless. Thank you.

Love your videos! They don't excuse themselves they just roll. Personally my favorites are on entropy, space-time and the mysteries in and between the two.

So glad to see a new video from you!

I have started this chapter yesterday and i am having some problems for clear concept and thinking about Eugene videos..... And suddenly this video appears to my notification..... TELEPORTATION WOW!

Thank you for your amazing videos! A question about 5:57: you say that because the work done depends only on initial and final state of the system (you assume thermal equilibrium?) then you derive that the slope of S must be 0. How did you infer that from the first point?

I would love to see you do a video on Hamilton-Jacobi theory and/or pilot wave theory

Whenever I see lagrange my mind reverts to ZZ Top and I go, "a Haw Haw Haw Haw"

I really liked the touch of having an orchestral adaptation of Hungarian Rhapsody no. II here, because I played sections on the piano when I was 19. It was very predictable that they gave the 64th note cadenza to the flute section, but not so predictable that they would replace some of the grace notes with a dotted rhythm. I didn't understand what a Lagrangian was, but I did learn some things about linear algebra!

Totally love these videos. Narrating excellent too. Can see a lot of work has gone into explaining the concept. Great stuff as usual!

Yay! New video by the master of physics videos. Great work as usual, Eugene and Kira.

Brilliant, subscribed! This has to be the best demonstration thus far, great channel!

Damn, I recently got taught this subject in my class and the past few weeks I've been struggling with the intuition for the Lagrangian, this video is actually such a coincidence. I'll have to rewatch it several times though, this is a tough one.

I always suggest your channel to every living being that walks on this earth (especially to people in my university) and have convinced many to subscribe to you. This amazing video proves to me once again why you are by far the most underrated and underappreciated channel on KZfaq and i fear the time that you will not upload your next video. Keep up the good work

That was brilliant! It so interesting to actually get an intuitive feeling for such a mysterious and beautiful equation.

I have no idea how many times I've watched this by now, but I love it. Thanks.

Thank you for your amazing teaching video. I'm wondering if there is proof for more independent variables. I've searched on the internet but don't find the full proof. Thank you in advance.

Absolutely amazing, thank you for such a wonderful animated explanation. Will rewatch and make some proper notes, that was excellent :D

This is even harder to understand than the mathematical proof

Instant subscribe. As someone who is struggling through learning lagrangian mechanics right now, this video was invaluable, especially the explanation of 14:28 of why one must take the derivative with respect to time of the second term

Excellent work!! Go on with the excellent videos

Very clear and informative video, as always!

superb stuff as always !......perhaps even your best yet

Perfect timing... Just began this in classical mechanics, thanks!

OMG I love your music!

Love your videos, thanks for the headache...

I can follow most of his videos. But master made this one tough.

I love how you start by generalizing how new theorists need to come up with new equations of lagrangian. Then you go to specify that you actually are explaining and treating the derivation of lagrangian for all possible variables in order to understand how to use lagrangian. You are giving us the actual tools 😍😍😍😍

Again, great work. I know this is a physics channel, but I must comment: I appreciate the music choices you make - along the aesthetics of the animations it is part of why your videos are so fantastic. This time too the individual songs are great, but I wish there were not so many different genres mixed in one video. Just my opinion - take it or leave it.

Great. Could You do the same about constrained variations and second variation? Best regards

Again, another great video about physics.

Thank you for making a new video

I get wayy too much excited when there's a new video

great video will look forward to qft video soon.

Really nice video. People may need to watch it a few times while making notes, but everything is there.

I am studying Lagrange euler and Newton euler in my robotics for dynamic motion and suddenly you make this video. Thank you for the visual explanation.

Can you please explain why the slope of the action/change in path graph has to be 0 for the actual path if the work done depends only on the initial and final state (6:11)?

Master had invented new system in educations. He/she uses colors for showing numbers (values)!!! I have been never seen this method before in my whole life. This method just simplfies and make more intuitive in complicated situations. Thanks alot for your free and briliant education

Great Please we need crash course about mathematical modelling science

Very nice as an intuitive explanation of Lagrangian. Never disappointed in these great videos. Can we please have a similar one on intuitive explanation of Hamiltonian? In which cases is Lagrangian or Hamiltonian more appropriate?

I really liked this video. I agree that it is not that intuitive for a newcomer but for someone studying the topic or having studied it, it is a great visualization

What the hell. Why is this video SO good. Goddamn. Came to the comments section to literally complain about what incredible quality this video is when surprise comment by Michael Stevens! Always a pleasure to see that

Wow glad to see what the lagrangian is! I’ve only heard of the name but not the maths! So cool!

After long time I have enjoyed this video....

Nice vid. It reminds me of using PID controllers in various applications in industrial businesses. Explaining the basics might make a nice vid. Multivariable controllers and feedforward controls are other useful applications of first and second deritive controls. Its easier to learn when you have a practical example in my opinion.

Stunning. This is educational masterwork.

I love your videos, but I would also enjoy knowing some practical applications for these equations.

thank you for your brilliant work, please what program you use to realize this animations

it's just amazing. thank you so much

Are you actually a teacher/University scholar for physics? These videos are so insanely helpful

Bro I just started learning Lagrangian Mechanics and this video blows my mind, greetings from Berlin!!

Love the animations it brings the maths alive ! What software did you use?

Oh my God how beautiful, elegant, eloquent and majestic your courses are in 3d animation. I dreamed of carrying out such courses in mathematics since I bought a PC in 2006. But alas, my knowledge in 3d animation is strictly nil. Excuse me for making a very small remark whose reasons are very big, very important and very deep concerning the way the brain learns. For the learning of the brain to be easy, clear, without ambiguity and without confusion, the information must reach it in order, point by point, step by step, in space and in time. That's to say: - from the past to the future. - from top to bottom. - from right to left. - from the simplest concept to the most complex. - in as many steps as possible. - without erasing, without replacing, and without inserting a step into another. - without going back to the top to view information. - etc ... The informations in the video entitled "L'algèbre et les mathématiques avec des animations 3D faciles à comprendre" are too difficult to follow, too difficult for a beginner in mathematics to understand. See above to understand why. I hope that your next videos will be made in the way I described. THANKS.

Really great video. Can you make a video about the Klein Gordon equation and the Dirac equation? thanks

Beautiful! Explained wonderfully

really hard concept to understand, but the video helped me to get my understanding to an above level. thanks.

Does hamiltonian equal to energy for all cases, if not, which cases are exceptions

Hey great video thanks for sharing, quick question couldn’t the slope of the blue be zero at a local maxima ?

So many questions... Why is time not considered as a variable/dimension? I mean why it is X and X', but not X and T? Is it because by definition L = T - V and those do not depend on time? And what is the physical meaning behind T - V? Where does it come from, why would I be interested in this difference? Or is it just a neat way to mathematically define the Lagrangian?

Great job Eugene! I know you state in the start of the video that you want to don't want to focus on the Lagrangian for any one specific theory but how the Lagrangian is used to predict the behavior of a system, however I think it would be nice to tie in an example at the end with a simple pendulum or mass spring damper just so we can see the theory in action (no pun intended). Thank you for all your videos!

you deserve much more views and subscribers

fantastic video, more advanced but also a more advanced topic

thanks for the video

Eugene how do we know the volume of a black singularity is zero? How to we know it's not asymptotically approaching zero? Thank you for all the videos.

Brilliant video, love it. What I don't get is that if we are dealing with physical laws where the total work done depends only on the initial and final state of the system, and not on the path in between, then why must the true actual path of the system be at a point where the slope is zero on the graph showing action against change in path. Also, as there are 3 points on the graph shown that are stationary, does this mean there are 3 different possible paths in the example given.

Thanks for the video. What is the music in the backhround please?

Absolutely wonderful! You left just enough to think about to make one understand. Thank you! I couldn’t really understand other explanations and they are no of use for me. Universities’ online lectures are too long as they always are spanning across hours with the inappropriate pace they have because no students already understand the theory. I mean lectures in unis would be of much better use of students were first given great theoretical explanation and then during lectures students could ask questions and make proposals and interact with the professor. Anyway, wonderful video!

Muito obrigado pela aula. Esta é uma apresentação de ótima qualidade.

can you make a video on the critical point and on the triple point?

Superb intuitive "feel" indeed. However, just at about 15:59, the net "increase" in action is actually the functional derivative of the action integral: please note that the entity is dimensionally different from "Action", per se. Also, for a classical Lagrangian system with independent generalized coordinates {q}, q-dot = dq/dt; thus the ordinary (= total) and the partial derivatives of " q " with respect to the time " t " both are congruent. Of course, for fields and multivariate problems, the partial derivatives will occur, as you have so rightly pointed out. It is a remarkably lucid video-clip that would instill motivation AND confidence into students to learn and explore theme with ramifications !!!

@Physics Videos by Eugene Khurtoryansky That was awesome! I didn't go to school really but I have always enjoyed reading history so I have learned a lot anyways. I rather enjoyed the seeing the 3 variable graph rendered as a flat graph and I was wondering the rules that allow that replotting is that what is meant by the term "translation" or "translation matrix"? Would it be correct to say the reason the equation must equal 0 to be correct is any other value means a variable was misidentified and skewed what could be called an attempt to balance the books? I rather like the way each added variable while still acquiring a final sum of 0 is another point of corroboration- the idea that identifing the correct value of each variable will confirmed by when combined the correct answer is 0 is rather amusing. Great sound track as well.

Really brilliant. Yes, you need Lagrangian understanding. There is no shortcut to spending lots of time and effort in studies. For those who have will thoroughly enjoy this

Thank you for the explanation!

Very good, simple coherent and well articulated, helped me immensely. Small criticism though, when you address the case where dL/dx' is negative at two points thus increasing the action, its a bit vague and not well integrated. Thank you very much for your efforts, greatly appreciated.

Nice visual representation of the Lagrangian, which is a very difficult topic!

This is a great video. It is the clearest explanation that I’ve yet come across. It would be helpful if you could change the color of various points on the Y-Axis, so that we can correlate the color of the dots on the charted line to the magnitude when looking at the graph from an oblique angle. Thanks.

Beautiful as always.

Hi, great work as always! Can you make a video where you explain the concept of Lagrangian density and the application on QFT?

Please do a video on the Hamiltonian, and also give a touch to compare Lagrangian and Hamiltonian.

Great video!!! However, I do have some questions: at 13:14, why is the amount by which the Lagrangian function will change for this point equal to ∂L/∂x, instead of dx·∂L/∂x, with dx denoted by ''the change amount of particle's position x''? Also, why is the amount by which the Action will increase equal to that amount too, instead of dt·dx·∂L/∂x when Action can be expressed as ∫Ldt? I would be truly grateful if someone could answer for me.

thank you so much! thanks to this video, I understood Lagrangian more accurately.

i dont know which level education part it's but i understood the lagrangian theroy!! Thank for the videos!

This was fairly abstract, especially considering your other uploads. Still enjoyed it though and I’m looking forward to the QFT video(s) coming in the future.

5: 37 Ok, what do you rigurously mean by "Change in path"?