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.
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.
Khutoryansky teaching philosophy: You never really learn something until you make a full-color computer graphics animation of it set to classical music.
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.
Important News: I will soon be enabling a UA-cam 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 UA-cam 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.
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!
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.
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.
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!
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!
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 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 😍😍😍😍
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
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!
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 !!!
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
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.
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.
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 UA-cam. I do want to be clear though, I think that you’re doing good work, and you should definitely keep at it.
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.
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
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 UA-cam 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.
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!
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.
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
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?
I offer you my sincere and deepest gratitude for this wonderful intellectual creation of yours and taking your precious time in doing so. Keep doing it.Be blessed
I really love that way to teaching about Lagrangians!, It's more powerful than any teaching way I've had ever used. I hope someday high-ranking universities like MIT or Harvard use that way to teaching, It will make better understanding,better visualization to physics, which will help students to solve hard problems easily and in a way that make physics❤ enjoyable. Thank you, You're Master😀.
So we are trying to figure out the "path" by representing the position of a molecule as an independant variable and the velocity as another independant variable in a separate position/velocity space and making the value of the langrangian be a dependant function on velocity and position represented as a 3d function. Then you take partial derivatives along each plane (position/velocity plane) and setting change in position - change in velocity = 0 the minimum in the optimization procedure represents the original "path". The real question is finding the langrangian function itself o.o. I suggest putting all the different subspaces in separate parallel windows with a highlighted box to the one you are referring to. Switching between the different subspaces too quickly without indicating which one you are referring to throws people off.
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.
In case you are interested in suggestio for future videos; what about a visual representation of an atom? How it looks and why it looks the way it does. Neil deGrasse Tyson used the incorrect Bohr model in Cosmos, which was left decades ago. According to the newer model, the electron cloud is a standing spherical wave in 3D, where it jumps to different "orbits" based on its energy content. This is also the reason why the different elements can only produce a limited number of colors. Interesting stuff, but hard to visualize.
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?
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?
L = T - V is just the form of langragian that gives Newton’s laws of classical mechanics. Take a more complicated lagrangian and you get (say) relativistic electrodynamics. The Euler-Lagrange has nothing to do with any of these theories, it’s just the equation that minimizes a path integral. It even has many applications in pure mathematics and other fields, it’s beyond physics.
Once E= mc^2 popped up, almost everyone recognize it, but in order to get there, you have Field Theory Equation on your way. Lots of best Mathematicians & Physicists worked hard & intense on the subject matter at the time to get it done. Einstein was working 20 years long for a uninfied Field Theory. Euler Lagrange least action is Not that hard ( like field theory ), but you need a good understanding of -----> Eulers " e " , Lagrangian means of Energy Transfer ( KE - PE ) described as a curve , & finally S ( l , t) called " least action " , which is equal to the area under the Lagrangian curve according to Formula : ( S = integ t1 to t2 of L . dt ). Hope it helps😊
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.
A visual explanation is the key to a true understanding of many different concepts. You do a lot of great work. What I would like to suggest is a change of background music, because the one with classical music is irritating for me. Maybe some light electronic music just like on the 3Blue1Brown channel.
With much due respect and gratitude for these videos and artwork, but respectfully the music does not tell the same story as the animations...nor is the music background music. Thanks again.
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 ua-cam.com/video/gcvq1DAM-DE/v-deo.html
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 realize I know nothing with watching these videos without already learning it. I watched this like a couple months ago and was like nice. Learning about lagrangians now and still am lost, but am like cool
Top tier maths for top tier physics. You will stumble on the concept of "Lagrangian" over and over if you are interested in fundamental physics, so it's a very good aid but on its own it's a bit "arid" (as maths always are).
They're acting as another "axis" but he's run out of spacial axes to represent it. You could think of it as a 4th numerical parameter (dimension) in a graph where the spacial dimensions already represent x, xdot and t. The colour represents change in dxdot/dt, the second derivative.
The UA-cam 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: ua-cam.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.
Everything is connected QM-Time, all variables constitute a synchronised, axial-tangential multiphase-state of omnipresent probability, infinitely distributed but focused on axies of Superspin Quantum Operator(s) modulated sync in Temporal Superposition-singularity.., ie Polar-Cartesian Coordination of elemental frequencies and amplitudes. -> Timing-spacing->Spacetime Dimensionality. So the Nomenclature used should reflect the operational intention. Eg the symbolic clock in this video, clocking-spacing time duration/displacement, shares a common synchronous axis of "staic" (Virtual Work) vectors, of numerically proportional dimensional sync, 3D dominance, and multiphase-state Time rates. The use of "Time" in the video is an abstract convention in which the local resonant ground state harmonic is and assumed zero rate of change/difference (ie =>.dt/universal zero axis), and the motion of atomic elemental properties set the empirical rules for the standards of measurements, so, as has always been known, at least in empirical experiential evidence, "All is Vibration" , e-Pi-i rationalization/resonance = QM-Time modulation substantiation, from the eternity-now "clocking", or self-defining, Principle. This video is a good illustrative example of the fractal quantum bubbles of naturally occurring "spinfoam"
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)?
I have the same doubt. Did you figure it out? I guess it has something to do with time going in the positive direction but not able to put the thought process completely.
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!
From the mathematically inclined perspective, this video was totally amazing! I loved it, seriously. However I feel like if I were to send it to my friend they would be lost. How the hell do we tell our friends about this? I mean it as an open question for us all, because this explanation is beautiful in the mathematical sense, but how do we tell the non-mathematical about this beauty? Explaining these things is the central struggle of my life I think. lol And no offense meant, Eugene. Some of your videos have explained deep things to me, in a way I can finally understand. I just have come to realize you and I are similar in a way most people are not. :)
With all due respect this video avoided all of the mathematically beautiful aspects of the theory. I really don’t mean to be rude but if this is your idea of mathematical beauty then I dare say that you aren’t as inclined as you think.
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!!
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.
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.
Khutoryansky teaching philosophy: You never really learn something until you make a full-color computer graphics animation of it set to classical music.
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
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
Thanks for putting effort in educating people, here is my comment.
Thanks.
Important News: I will soon be enabling a UA-cam 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 UA-cam 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 UA-cam 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
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.
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!!!
I sincerely wish to thank you Eugene for this thoughtful and inspiring video visualization lecture. It is right on time.
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.
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.
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
This came along at the perfect time for me. Visual depiction of the least action principle in terms of Euler-Lagrange equation. Nailed it!
I am glad you liked my video.
Personaly, that's your hardest video to understand up to now.
If you like this video, you can help more people find it in their UA-cam 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?
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!
Whenever I see lagrange my mind reverts to ZZ Top and I go, "a Haw Haw Haw Haw"
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.
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.
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.
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.
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!
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.
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.
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 !!!
Didn't understand everything but that right there, the music, the animation the clarity that is perfection thank you for sharing.
I am glad you liked my video. Thanks.
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.
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.
Just leaving a comment because it increases priority in youtube's search algorithm
Thanks.
@@EugeneKhutoryansky happy to help... these videos you make are really helpful teaching tools, and they're really well made
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.
I would love to see you do a video on Hamilton-Jacobi theory and/or pilot wave theory
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 UA-cam. I do want to be clear though, I think that you’re doing good work, and you should definitely keep at it.
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.
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
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.
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 UA-cam 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.
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.
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? 😂
Such beautiful explanatory animations, and even though I cannot understand all the topics I appreciate them nevertheless. Thank you.
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.
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.
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
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 offer you my sincere and deepest gratitude for this wonderful intellectual creation of yours and taking your precious time in doing so.
Keep doing it.Be blessed
Thanks.
I really love that way to teaching about Lagrangians!, It's more powerful than any teaching way I've had ever used. I hope someday high-ranking universities like MIT or Harvard use that way to teaching, It will make better understanding,better visualization to physics, which will help students to solve hard problems easily and in a way that make physics❤ enjoyable.
Thank you, You're Master😀.
Thanks.
Stunning. This is educational masterwork.
Thanks for the compliment.
So glad to see a new video from you!
힘내주세요. 포기하지말아요. 이 동영상은 아주 멋져요. 도와주셔서 고마워요❤
So we are trying to figure out the "path" by representing the position of a molecule as an independant variable and the velocity as another independant variable in a separate position/velocity space and making the value of the langrangian be a dependant function on velocity and position represented as a 3d function. Then you take partial derivatives along each plane (position/velocity plane) and setting change in position - change in velocity = 0 the minimum in the optimization procedure represents the original "path". The real question is finding the langrangian function itself o.o. I suggest putting all the different subspaces in separate parallel windows with a highlighted box to the one you are referring to. Switching between the different subspaces too quickly without indicating which one you are referring to throws people off.
you deserve much more views and subscribers
Thanks.
Again, another great video about physics.
Thanks for the compliment.
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.
Liszt Hungarian Rapsody made it even better!
Henry you are showboating.
thank you, I was looking for the name.
no
Thanks,greetings from Turkey
Thanks. Greetings from the U.S.A.
Wow glad to see what the lagrangian is! I’ve only heard of the name but not the maths! So cool!
amazing video
Thanks
In case you are interested in suggestio for future videos; what about a visual representation of an atom? How it looks and why it looks the way it does. Neil deGrasse Tyson used the incorrect Bohr model in Cosmos, which was left decades ago. According to the newer model, the electron cloud is a standing spherical wave in 3D, where it jumps to different "orbits" based on its energy content. This is also the reason why the different elements can only produce a limited number of colors. Interesting stuff, but hard to visualize.
Perfect timing... Just began this in classical mechanics, thanks!
Glad I finished the video just in time. Thanks.
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?
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?
L = T - V is just the form of langragian that gives Newton’s laws of classical mechanics. Take a more complicated lagrangian and you get (say) relativistic electrodynamics. The Euler-Lagrange has nothing to do with any of these theories, it’s just the equation that minimizes a path integral. It even has many applications in pure mathematics and other fields, it’s beyond physics.
After long time I have enjoyed this video....
That was brilliant! It so interesting to actually get an intuitive feeling for such a mysterious and beautiful equation.
Thanks.
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 dont know which level education part it's but i understood the lagrangian theroy!! Thank for the videos!
Please do a video on the Hamiltonian, and also give a touch to compare Lagrangian and Hamiltonian.
Once E= mc^2 popped up, almost everyone recognize it, but in order to get there, you have Field Theory Equation on your way. Lots of best Mathematicians & Physicists worked hard & intense on the subject matter at the time to get it done. Einstein was working 20 years long for a uninfied Field Theory.
Euler Lagrange least action is Not that hard ( like field theory ), but you need a good understanding of -----> Eulers " e " , Lagrangian means of Energy Transfer ( KE - PE ) described as a curve , & finally S
( l , t) called " least action " , which is equal to the area under the Lagrangian curve according to Formula : ( S = integ t1 to t2 of L . dt ). Hope it helps😊
Excellent work!! Go on with the excellent videos
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.
A visual explanation is the key to a true understanding of many different concepts. You do a lot of great work. What I would like to suggest is a change of background music, because the one with classical music is irritating for me. Maybe some light electronic music just like on the 3Blue1Brown channel.
You lost me at 00:01
that's quite an achievement ... I was lost at 00:00
@@AbdulelahAlJeffery cuz I'm not as dumb as you.
@@pirateman1966 🤣😂
Lagrange Aubergine
I was lost at 18:21
fantastic video, more advanced but also a more advanced topic
OMG I love your music!
With much due respect and gratitude for these videos and artwork, but respectfully the music does not tell the same story as the animations...nor is the music background music. Thanks again.
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 ua-cam.com/video/gcvq1DAM-DE/v-deo.html
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?
Muito obrigado pela aula. Esta é uma apresentação de ótima qualidade.
Very clear and informative video, as always!
Thanks for the compliment.
Our real teacher is back with a new video. If any body ask me awesome person in my life Eugene is always in first position :)
Thanks for that really great compliment.
Plz plz plz plz plz ......Cover as much as physics and maths.I don't know how can I tell you Thanks...
I can't understand why d/dt appears in the equation..
Thank you so much :):):)
That is the question! We'll leave dL/dx just like that, but dL/dx' we have to differentiate wrt time. Why??
do you have a phd in physics? it seems that you are so smart and creative...
You amaze me every time
I realize I know nothing with watching these videos without already learning it. I watched this like a couple months ago and was like nice. Learning about lagrangians now and still am lost, but am like cool
Are you actually a teacher/University scholar for physics? These videos are so insanely helpful
thank you so much! thanks to this video, I understood Lagrangian more accurately.
Glad my video was helpful. Thanks.
1:43 X, Y, and Z are dependent variables the way you have diagrammed it. T is the independent variable.
No, that is not the case. X, Y, and Z could be the position of a free particle, without any constraints, experiencing a force.
I get wayy too much excited when there's a new video
I have no idea what this video was about. Perhaps some day I will.
It's a very interesting topic.
Top tier maths for top tier physics. You will stumble on the concept of "Lagrangian" over and over if you are interested in fundamental physics, so it's a very good aid but on its own it's a bit "arid" (as maths always are).
How does changing the colors make sense? Are they random?
They're acting as another "axis" but he's run out of spacial axes to represent it. You could think of it as a 4th numerical parameter (dimension) in a graph where the spacial dimensions already represent x, xdot and t. The colour represents change in dxdot/dt, the second derivative.
The UA-cam 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:
ua-cam.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.
Muchas gracias!
Everything is connected QM-Time, all variables constitute a synchronised, axial-tangential multiphase-state of omnipresent probability, infinitely distributed but focused on axies of Superspin Quantum Operator(s) modulated sync in Temporal Superposition-singularity.., ie Polar-Cartesian Coordination of elemental frequencies and amplitudes.
-> Timing-spacing->Spacetime Dimensionality.
So the Nomenclature used should reflect the operational intention. Eg the symbolic clock in this video, clocking-spacing time duration/displacement, shares a common synchronous axis of "staic" (Virtual Work) vectors, of numerically proportional dimensional sync, 3D dominance, and multiphase-state Time rates.
The use of "Time" in the video is an abstract convention in which the local resonant ground state harmonic is and assumed zero rate of change/difference (ie =>.dt/universal zero axis), and the motion of atomic elemental properties set the empirical rules for the standards of measurements, so, as has always been known, at least in empirical experiential evidence, "All is Vibration" , e-Pi-i rationalization/resonance = QM-Time modulation substantiation, from the eternity-now "clocking", or self-defining, Principle.
This video is a good illustrative example of the fractal quantum bubbles of naturally occurring "spinfoam"
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!
At 15:02 why will both the points go down only . Negative sign of the second term is not explained clearly.
I have the same doubt. Did you figure it out? I guess it has something to do with time going in the positive direction but not able to put the thought process completely.
Nice visual representation of the Lagrangian, which is a very difficult topic!
Thanks for the compliment about my visual representation.
So if I divide doing the dishes by the square root feeding the dog ...then I can find the value of my sisters bad breath !!!
Brilliant !
Thanks man !
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.
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!
From the mathematically inclined perspective, this video was totally amazing! I loved it, seriously. However I feel like if I were to send it to my friend they would be lost. How the hell do we tell our friends about this? I mean it as an open question for us all, because this explanation is beautiful in the mathematical sense, but how do we tell the non-mathematical about this beauty? Explaining these things is the central struggle of my life I think. lol And no offense meant, Eugene. Some of your videos have explained deep things to me, in a way I can finally understand. I just have come to realize you and I are similar in a way most people are not. :)
With all due respect this video avoided all of the mathematically beautiful aspects of the theory.
I really don’t mean to be rude but if this is your idea of mathematical beauty then I dare say that you aren’t as inclined as you think.