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!!
In this example in the video where both point are going down, the expression d(∂L/∂ẋ)/dt is positive. If we were to create a different example where both points are going up, the expression d(∂L/∂ẋ)/dt would be negative. In this new example, the total action would be increasing, but we can view this by saying that the total action is decreasing by a negative amount. That is, the total action is still decreasing by the value of d(∂L/∂ẋ) /dt. Please let me know if this explanation helps clear this up for you. By the way, congratulations on your extremely popular channel.
@@EugeneKhutoryansky Thank you! I really appreciate your reply. Very helpful. And thanks for these videos. You're the KING of visualizing the abstract -- I really appreciate what you're doing. If you don't mind, I have one more question: I see that d(∂L/∂ẋ)/dt is positive at 14:43 and that action decreases in the case shown, and so the minus sign in the EL equation makes sense. But what if our variation required a decrease in ẋ at time 1 and a subsequent increase at time 2 (so that both points moved 'uphill' at 14:43 instead of 'downhill'). In that case, wouldn't we have a positive d(∂L/∂ẋ)/dt and also an increase in action?
oh, and by the way, I think the intuitive approach used here is similar to Euler's original geometric method of the calculus of variations (as opposed to Lagrange's method which is more common in textbooks). I really like it! I wouldn't have discovered it without this video.
The reason we needed a positive variation in the velocity (ẋ) at time 1, and a negative variation in velocity (ẋ) at time 2 is because we had a positive variation in the position (x) in between these two times. For what you are describing to happen, we would instead need a negative variation in the position (x). Therefore, what we would end up having is the negative of the Euler-Lagrange equation. That is, we would have -(∂L/∂x)+d(∂L/∂ẋ)/dt = 0. And this equation is true when the Euler-Lagrange equation is also true, since the right side of the equation is zero in both cases. Please let me know if this answers your question. And thanks for the compliment about my visualizations. I am glad you like them. Although many people comment on how my visualizations are the best, most people have still never heard about my channel, and hence I have been struggling to attract more viewers.
Khutoryansky teaching philosophy: You never really learn something until you make a full-color computer graphics animation of it set to classical music.
Important News: I will soon be enabling a CZcams 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 CZcams 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
I would love to help with Portuguese subtitles. Hopefully other Brazilians and Portuguese speakers watch it as well =) I love you videos. Thank you for making them.
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.
I recommend you watch the earlier video in this series, which explains partial derivatives. There are no real shortcuts in understanding this kind of material.
@Michael It is pretty straightforward if you see that that x-dot is nothing but the velocity of particle. L is a function of position (x) and the velocity (v). Then proceed with whatever derivatives you need. Hope this helps a bit.
Your stuff is awesome! The visualizations and breakdowns really help me understand what others seem to take for granted. I no longer feel lost after watching a topic. The more, the better. Thank you!
The CZcams 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: czcams.com/users/timedtext_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.
Sinta-se livre, eu acabei dando uma pausa por que meu notebook quebrou, mas assim que voltar do conserto vou terminar a playlist de matemática. My laptop broke so I've stoped the traduction for a little bit, but soon I will be back to traduce the math playlist to portuguese.
Exactly. Nothing about this video can be marked with the word "intuitively", perhaps "graphically in slow motion". No example, no background, and links, no parable or comparison. What is the point of doing something for those who know it already?
Yeeeah, actually, as someone with what I feel to be a pretty okay grasp of Lagrangian mechanics, this actually increased my confusion. I mean, I think I get what this was trying to do for the most part, and the color shifts to represent partial differentiation was pretty neat, but overall I felt like this needed a lot more explanation for what the various visualizations were actually doing and saying. More importantly, I think it would have helped to use examples that map onto real, simple physical situations where the Lagrangian is useful, to help form some sort of physical intuition. Usually these videos provide some useful insights, but for me at least, thanks to the seemingly totally arbitrary example functions used, this was about as clear as mud.
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.
Well, those are not my main issues as "uninitiated" I assure you. I'd rather would like "concrete" examples of what "action" means and stuff like that, because all I can visualize is like "quantum vacuum in Einsteinian space-time" but still not able to tie the strings into something that somehow makes sense without a "physical" example: maths are fine... when they refer to real stuff, else they are just meaningless equations. So dots and clocks are not a problem themselves: as they are "physical-ish" and anyhow don't interfere with the mathematical representation, the problem is what does all this mean for a cubic nanometer of space-time or some other "real" thing?
@@LuisAldamiz if you start with newtons second law you can obtain "work-energy" and "impulse-momentum" equations, by integrating over distance and time respectively. Action is the quantity you get from integrating by both.
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.
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.
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!
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.
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!
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!
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
For simple explanation see Euler's original derivation. Also derived on my calculus of variations Udemy course , both Eulers geometric derivation and Lagrange's analytic derivation. E / L tells you something really quite simple.
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.
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
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 CZcams and i fear the time that you will not upload your next video. Keep up the good work
Thanks for helping to promote my channel and getting people to subscribe to it. I really appreciate that. And thanks for the compliment about my video.
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
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.
@@EugeneKhutoryansky I liked all the music in this video. Nice and fitting. I can't help but say that It squares the sense of wonder that the video would otherwise have.
The video is not only wonderous but also straight to the point - good educational material, even if it might take a rewatch or two to really get. But that's the lady mathematics for you.
I like classical music (well, Hungarians rhapsody is really Romantic, but the average person calls it classical anyway), but you use the same pieces over and over, and the flow doesn’t really mesh well with the video. I think it would be a lot better if you chose clips of pieces and edited them together so that it flows with the script better. Just things like when you pause to let something sink in, and then the music starts going crazy, and it’s distracting. It doesn’t matter as much for me since I can enjoy the pieces on their own, but I’m reluctant to recommend your videos to students that I TA because I feel like for most people that’s a big turnoff, and it doesn’t matter at that point how good your explanation is because they won’t watch it in the first place. I realize that attending to minutiae like this takes a lot, but it’s this sort of thing that separates the wheat from the chaff on CZcams. I do want to be clear though, I think that you’re doing good work, and you should definitely keep at it.
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.
Physics Videos by Eugene Khutoryansky I could always work through Lagrangian problems but I never truly understood why the equation works until now. Love the channel!
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 😍😍😍😍
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.
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
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.
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?
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!
Thanks for the compliment. I had initially planned on doing some examples, but I ended up not including them so as to keep the video down to a reasonable length. When people see that a video is extremely long, many people end up not watching it at all as a result.
Ich wohne auch in berlin , ich möchte infos zu * Titel Explizite Finite Elemente Methode * in meinem Studium in Maschinenbau deswegen ich gucke dieses Video, und was ist mit Ihnen?
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?
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
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 !!!
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!
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.
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.
A couple of questions ... @5:16, you have shown a plot of the {x,y,z} coordinates of a proposed path of the particle thru 3D space, along with a graph of the action vs. “changes in path”. As you stated, the action is calculated over the entire path from location P1 (initial) to location P2 (final). How do you reduce “changes in {x,y,z} coordinates” to a single value which represents the entire 3D path? Do you sum [Δx^2 + Δy^2 + Δz^2]^0.5 for all path points between P1 & P2?
I would love to see another video on gravity. Specifically on why time is the dominate factor, instead of curved space, for why space curves. Love the vids and music.
As you probably already know, I already have many videos on gravity. For example, I have a video that focuses on that question that is titled "Gravitational Time Dilation causes Attraction" at czcams.com/video/gcvq1DAM-DE/video.html
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.
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.
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)?
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).
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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!!
In this example in the video where both point are going down, the expression d(∂L/∂ẋ)/dt is positive. If we were to create a different example where both points are going up, the expression d(∂L/∂ẋ)/dt would be negative. In this new example, the total action would be increasing, but we can view this by saying that the total action is decreasing by a negative amount. That is, the total action is still decreasing by the value of d(∂L/∂ẋ) /dt. Please let me know if this explanation helps clear this up for you. By the way, congratulations on your extremely popular channel.
@@EugeneKhutoryansky Thank you! I really appreciate your reply. Very helpful. And thanks for these videos. You're the KING of visualizing the abstract -- I really appreciate what you're doing.
If you don't mind, I have one more question: I see that d(∂L/∂ẋ)/dt is positive at 14:43 and that action decreases in the case shown, and so the minus sign in the EL equation makes sense. But what if our variation required a decrease in ẋ at time 1 and a subsequent increase at time 2 (so that both points moved 'uphill' at 14:43 instead of 'downhill'). In that case, wouldn't we have a positive d(∂L/∂ẋ)/dt and also an increase in action?
oh, and by the way, I think the intuitive approach used here is similar to Euler's original geometric method of the calculus of variations (as opposed to Lagrange's method which is more common in textbooks). I really like it! I wouldn't have discovered it without this video.
The reason we needed a positive variation in the velocity (ẋ) at time 1, and a negative variation in velocity (ẋ) at time 2 is because we had a positive variation in the position (x) in between these two times. For what you are describing to happen, we would instead need a negative variation in the position (x). Therefore, what we would end up having is the negative of the Euler-Lagrange equation. That is, we would have -(∂L/∂x)+d(∂L/∂ẋ)/dt = 0. And this equation is true when the Euler-Lagrange equation is also true, since the right side of the equation is zero in both cases. Please let me know if this answers your question. And thanks for the compliment about my visualizations. I am glad you like them. Although many people comment on how my visualizations are the best, most people have still never heard about my channel, and hence I have been struggling to attract more viewers.
@@EugeneKhutoryansky YES! Thank you. Very clear. And I'll be doing my part to make sure more people find out about your videos!!
Khutoryansky teaching philosophy: You never really learn something until you make a full-color computer graphics animation of it set to classical music.
Important News: I will soon be enabling a CZcams 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 CZcams 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
I would love to help with Portuguese subtitles. Hopefully other Brazilians and Portuguese speakers watch it as well =)
I love you videos. Thank you for making them.
I hope there will be an explanation in Arabic or at least a translation in Arabic, please
I can help translating it to Russian or Ukrainian. If anyone is willing to cooperate, contact me via CZcams DMs in order for us to discuss the details
Hello there, Please enlighten us with videos about Poincarè ball and Hyperbolic space 🌸
i understanding better in hindi I love your videos
I always waiting to your videos you are awesome
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.
I recommend you watch the earlier video in this series, which explains partial derivatives. There are no real shortcuts in understanding this kind of material.
@Michael It is pretty straightforward if you see that that x-dot is nothing but the velocity of particle. L is a function of position (x) and the velocity (v). Then proceed with whatever derivatives you need. Hope this helps a bit.
If you like this video, you can help more people find it in their CZcams search engine by clicking the like button, and writing a comment. Thanks.
Your stuff is awesome! The visualizations and breakdowns really help me understand what others seem to take for granted. I no longer feel lost after watching a topic. The more, the better. Thank you!
Thanks.
Thanks
Thank you for the video! What about a video on the Hamiltonian?
will we get to see more new
videos regularly now?
The CZcams 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:
czcams.com/users/timedtext_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.
The traduction for brazilian portuguese is in action, soon we will start, probably by the math playlist first.
@@guilhermegondin151 Estou pensando em fazer daquele video do experimento com o Quantum Eraser.
Sinta-se livre, eu acabei dando uma pausa por que meu notebook quebrou, mas assim que voltar do conserto vou terminar a playlist de matemática.
My laptop broke so I've stoped the traduction for a little bit, but soon I will be back to traduce the math playlist to portuguese.
Please make a video on configuration space and phase space also. You are doing great job
Muchas gracias!
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.
Thanks. I am glad my videos have been helpful.
Thanks for putting effort in educating people, here is my comment.
Thanks.
this video was for those who already had an understanding about Lagrangian..
Exactly. Nothing about this video can be marked with the word "intuitively", perhaps "graphically in slow motion". No example, no background, and links, no parable or comparison. What is the point of doing something for those who know it already?
Yes lol. It was nice to get a more intuitive feeling of it after studying in classical dynamics
Yeeeah, actually, as someone with what I feel to be a pretty okay grasp of Lagrangian mechanics, this actually increased my confusion. I mean, I think I get what this was trying to do for the most part, and the color shifts to represent partial differentiation was pretty neat, but overall I felt like this needed a lot more explanation for what the various visualizations were actually doing and saying. More importantly, I think it would have helped to use examples that map onto real, simple physical situations where the Lagrangian is useful, to help form some sort of physical intuition.
Usually these videos provide some useful insights, but for me at least, thanks to the seemingly totally arbitrary example functions used, this was about as clear as mud.
It’s a complex topic
I like that these videos sometimes take a different t approach than you usually see in elementary videos teaching these topics
I sincerely wish to thank you Eugene for this thoughtful and inspiring video visualization lecture. It is right on time.
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.
I agree. Looks like a lot of fun with graphics, but I haven't looked at this math for a long time and I didn't get much out of it.
Well, those are not my main issues as "uninitiated" I assure you. I'd rather would like "concrete" examples of what "action" means and stuff like that, because all I can visualize is like "quantum vacuum in Einsteinian space-time" but still not able to tie the strings into something that somehow makes sense without a "physical" example: maths are fine... when they refer to real stuff, else they are just meaningless equations.
So dots and clocks are not a problem themselves: as they are "physical-ish" and anyhow don't interfere with the mathematical representation, the problem is what does all this mean for a cubic nanometer of space-time or some other "real" thing?
@@LuisAldamiz if you start with newtons second law you can obtain "work-energy" and "impulse-momentum" equations, by integrating over distance and time respectively. Action is the quantity you get from integrating by both.
Please make a video
halp
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.
Whenever I see lagrange my mind reverts to ZZ Top and I go, "a Haw Haw Haw Haw"
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.
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!
So glad to see a new video from you!
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!
I am glad my video was helpful. Thanks.
Personaly, that's your hardest video to understand up to now.
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.
Thanks for that really great compliment and I really appreciate the donation. Thanks!!!
Yay! New video by the master of physics videos.
Great work as usual, Eugene and Kira.
Thanks.
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!
Glad I finished my video just at the right time.
Totally love these videos. Narrating excellent too.
Can see a lot of work has gone into explaining the concept.
Great stuff as usual!
Thanks for the compliments.
Brilliant, subscribed! This has to be the best demonstration thus far, great channel!
Thanks for the compliment and I am glad to have you as a subscriber.
That was brilliant! It so interesting to actually get an intuitive feeling for such a mysterious and beautiful equation.
Thanks.
superb stuff as always !......perhaps even your best yet
Thanks for the compliment. I am glad you liked my video so much to think that it might be my best one so far.
I have no idea how many times I've watched this by now, but I love it. Thanks.
Thanks. I am glad that you liked my video that much.
Absolutely amazing, thank you for such a wonderful animated explanation. Will rewatch and make some proper notes, that was excellent :D
Thanks for the compliments. I am glad you liked my video.
I would love to see you do a video on Hamilton-Jacobi theory and/or pilot wave theory
Perfect timing... Just began this in classical mechanics, thanks!
Glad I finished the video just in time. Thanks.
I can follow most of his videos. But master made this one tough.
Think of the movements of chess pieces through time in a chess game.
Very clear and informative video, as always!
Thanks for the compliment.
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!
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
Thanks.
Love your videos, thanks for the headache...
This is even harder to understand than the mathematical proof
For simple explanation see Euler's original derivation. Also derived on my calculus of variations Udemy course , both Eulers geometric derivation and Lagrange's analytic derivation. E / L tells you something really quite simple.
Ya
Think of it as Elements in A ABSTRACT group
Excellent work!! Go on with the excellent videos
Thanks.
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.
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
Glad to have you as a subscriber. And I am glad my video was helpful.
Muito obrigado pela aula. Esta é uma apresentação de ótima qualidade.
Thank you for making a new video
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 CZcams and i fear the time that you will not upload your next video. Keep up the good work
Thanks for helping to promote my channel and getting people to subscribe to it. I really appreciate that. And thanks for the compliment about my video.
Again, another great video about physics.
Thanks for the compliment.
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
Thanks for the compliment.
After long time I have enjoyed this video....
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.
Thanks for the compliment about my video, and I am glad that there is at least one person who likes my choice of music for the video.
@@EugeneKhutoryansky I liked all the music in this video. Nice and fitting. I can't help but say that It squares the sense of wonder that the video would otherwise have.
The video is not only wonderous but also straight to the point - good educational material, even if it might take a rewatch or two to really get. But that's the lady mathematics for you.
Thanks.
I like classical music (well, Hungarians rhapsody is really Romantic, but the average person calls it classical anyway), but you use the same pieces over and over, and the flow doesn’t really mesh well with the video. I think it would be a lot better if you chose clips of pieces and edited them together so that it flows with the script better. Just things like when you pause to let something sink in, and then the music starts going crazy, and it’s distracting. It doesn’t matter as much for me since I can enjoy the pieces on their own, but I’m reluctant to recommend your videos to students that I TA because I feel like for most people that’s a big turnoff, and it doesn’t matter at that point how good your explanation is because they won’t watch it in the first place. I realize that attending to minutiae like this takes a lot, but it’s this sort of thing that separates the wheat from the chaff on CZcams. I do want to be clear though, I think that you’re doing good work, and you should definitely keep at it.
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.
Beautiful! Explained wonderfully
Gald you liked my explanation. Thanks.
Physics Videos by Eugene Khutoryansky I could always work through Lagrangian problems but I never truly understood why the equation works until now. Love the channel!
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 😍😍😍😍
Thanks.
OMG I love your music!
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.
Glad I made the video at the right time for you. Thanks.
Really cool man!
Thank you for the explanation!
Thanks.
Stunning. This is educational masterwork.
Thanks for the compliment.
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
Really nice video. People may need to watch it a few times while making notes, but everything is there.
I am glad you liked my 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.
Beautiful as always.
Thanks.
great video
will look forward to qft video soon.
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?
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!
Thanks for the compliment. I had initially planned on doing some examples, but I ended up not including them so as to keep the video down to a reasonable length. When people see that a video is extremely long, many people end up not watching it at all as a result.
Bro I just started learning Lagrangian Mechanics and this video blows my mind, greetings from Berlin!!
Ich wohne auch in berlin , ich möchte infos zu * Titel Explizite Finite Elemente Methode * in meinem Studium in Maschinenbau deswegen ich gucke dieses Video, und was ist mit Ihnen?
@@khalilibraheam1537 Physik Student ;)
I get wayy too much excited when there's a new video
Thanks for your work
Thanks.
really hard concept to understand, but the video helped me to get my understanding to an above level. thanks.
Wow glad to see what the lagrangian is! I’ve only heard of the name but not the maths! So cool!
i dont know which level education part it's but i understood the lagrangian theroy!! Thank for the videos!
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 love your videos, but I would also enjoy knowing some practical applications for these equations.
thank you so much! thanks to this video, I understood Lagrangian more accurately.
Glad my video was helpful. Thanks.
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
it's just amazing. thank you so much
Thanks.
thanks for the video
fantastic video, more advanced but also a more advanced topic
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 !!!
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!
Thanks. I am glad you liked my video.
Great
Please we need crash course about mathematical modelling science
you deserve much more views and subscribers
Thanks.
thank you, very intuitive indeed...
Thanks,greetings from Turkey
Thanks. Greetings from the U.S.A.
You are just great.
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.
Really great video. Can you make a video about the Klein Gordon equation and the Dirac equation? thanks
I will add the Klein Gordon equation to my list of topics for future videos. The Dirac equation was already on the list. Thanks.
do you want humanity to end? 😂
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.
A couple of questions ...
@5:16, you have shown a plot of the {x,y,z} coordinates of a proposed path of the particle thru 3D space, along with a graph of the action vs. “changes in path”.
As you stated, the action is calculated over the entire path from location P1 (initial) to location P2 (final).
How do you reduce “changes in {x,y,z} coordinates” to a single value which represents the entire 3D path?
Do you sum [Δx^2 + Δy^2 + Δz^2]^0.5 for all path points between P1 & P2?
Hi, great work as always!
Can you make a video where you explain the concept of Lagrangian density and the application on QFT?
Thanks. Yes, that is on my list of topics for future videos.
I would love to see another video on gravity. Specifically on why time is the dominate factor, instead of curved space, for why space curves. Love the vids and music.
As you probably already know, I already have many videos on gravity. For example, I have a video that focuses on that question that is titled "Gravitational Time Dilation causes Attraction" at czcams.com/video/gcvq1DAM-DE/video.html
amazing video
Thanks
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.
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.
Great job.
Thanks.
Love the animations it brings the maths alive ! What software did you use?
I make my 3D animations with "Poser." Thanks.
Cool! This looks like interesting stuff
Thanks.
thank you for your brilliant work, please what program you use to realize this animations
Thanks for the compliment. I make my 3D animations with "Poser."
Thank you so much !
You are welcome and thanks.
It's great ! thank you a lot!
Thanks.
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)?
Yes, I'm also struggling to understand this!
Excellents videos i like the easy way that you explain items and terms are difficult
Liszt Hungarian Rapsody made it even better!
Henry you are showboating.
thank you, I was looking for the name.
no
Great. Could You do the same about constrained variations and second variation? Best regards