If you're looking for more on Lagrangian mechanics, there's a whole chapter in my eBook on it (Chapter 4): gumroad.com/l/ubSc I even use the double pendulum as one of my examples, if you were itching for more detail. 🤓
I bought the book! :) I had encountered the Lagrangian before, but it was the Euler-Lagrange equation applied to describe some quantum energy weirdness that I didn't understand at all. I didn't even know that Lagrangian thing existed, plus, it seemed strange to me that it was used there - Lagrange died way before Quantum Mechanics even existed. I'll be happy to learn it from your book :)
Love the asylum, great work. could you maybe do a video on faster than light neutrino's? Or Maybe suggest some helpful info sources. Everything I've seen says this phenomenon is a myth but then what is the deal with the super kamiokande neutrino detector. Really hitting a wall here. Any help would be appreciated.
Yeah, I'd love that too. I've been asking stuff about QM a lot and people keep mentioning Hamiltonian mechanics, but I don't know anything about it. I'd love a Science Asylum explanation!
Great video. When I discovered Langrangian mechanics, as a physics major, I was like, "holy shit! my life has been a lie!" You feel like a kid who has been playing with alphabet blocks, suddenly learning about literature.
@ Everything is NOT just given. Sure, some introductory physics textbooks will just give a bunch of equations without explaining where they come from, but that's just poor teaching. All of those equations had to be derived and experimentally verified. Why is physics complicated? Because its the study of the physical world and the physics world is complicated.
@ Newtonian physics isn't that complicated, true, but that's the simplest type of physics. Things get a lot more complicated when you move on to things like general relativity, quantum mechanics, etc., in large part because the math required is quite advanced.
@ I don't know who you're referring to, but why are you assuming that biology and physics can't _both_ be complicated? I don't know much biology myself, but honestly, _any_ major field of study is likely to get complicated -- if it were super simple and easy to understand it wouldn't be something people spent years or even decades studying to understand. Furthermore, people have different talents and so some people will find some subjects much easier to understand than others. A topic that seems incredibly complicated and hard to understand for one person may seem quite simple and intuitive to someone else. Heck, there are lots of things that seem really simple and intuitive to me know that I once found really difficult to comprehend. Anyhow, just because something gets complicated doesn't mean it's impossible to understand or not worth learning.
Look.... Many many times have I praised you before. Don't get tired of it because holy cow... Your videos are spectacular. You can explain very deeply, very easily and without losing touch with many many important aspects of science. It's a very honest simplification with wonderful results. As a physics master and a teacher, I'm always amazed. I imagine it takes a lot of hard work from you. So congratulations. Really.
@@ScienceAsylum I can only imagine!! But hey... Wanting to be more productive is only natural. Every hard work brings that feeling. I, for one, think you release videos in a very good pace. Specially if considering this high quality of content
@@ScienceAsylum You can do it! 👍 I live in my car atm (luxury, station with a mattress and no rent (crazy expensive)) in Reykjavik cuz I nearly went too crazy (also let my underground culture exploit me so I could learn a bit about it how it functions.. de-functions (Its a bad hobby I know trying to save the world but being responsible and seeing it first)) haha but I am ok now just a little crazy (not dishonest) which is the only way to be. I still throw 20$ your way on patreon soon my potential friend. I watched your vids for an hour yesterday, its soothing. By the way..a favour please. I thought a bit about it when I was 14 and came to the conclusion that black holes gain much more mass than what they actually eat in kilograms.. cuz of all the energy (hot hot 'n fast fast) in the mass that it took with it "when" it merged with the singularity.. how am I wrong? Thanks for a grrreat channel. I have a bag full of food and going to my secret sober meeting in 1 hour so i'm not "fine" rather I am well and improving haha. Thanks for a great channel. Ps. Did you catch what I said two days ago about Han Solo and the kessel run? I made it on the spot in my car and I am a little proud of it if I say so my self. Pps. "How can you make as many as possible undestand something as well as possible in the shortest amount of time" is in my opinion the basics for "The science of explaining" is. No professor or teacher or anyone has been able to tell me what that science is called.. But you are mastering it. 👊🐶🌎🧙♂️👍
I hope you do not feel I am oversharing... just telling a bit.. Thanks. By the way. The lack of space in my comment obve.. for you to read it well and the extra "is" .. are totally intentional..ehm! (not)👊😂 for my artistic freedom wings of hotness must not be damped with stale perfexion.. ola. (I am a trained proofreader (in my language) and I used to make book's texts look good on page and ready for printing g-dangit! (Also only stuck my toes in the jacuzzi of the underground for a few weeks lately --after my wife left in april cuz i drank too much beer (true and we together again) --and i let in the mother of my friend who brought criminals with her that lied to me and I pity them for weeks and helped haha)) Haha! Thanks again.. It feels great to share and tell you guys how awesome I think this Youtilube Asylum thing is and them progresses it is proliferating. 12 minutes until meeting starts.. Have a good day guys! Thank you. And now for something completely different. In case you missed it. Alternatino rules! 😂 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-1j4rrgr0KeU.html
Making things easy isn't easy, especially while holding on to accuracy... and often requires the whole picture while keeping things brief. The result is brilliant simplicity.
What I like most about lagrangian mechanics is how it treats forces such as surface reaction (normal force) and string tension. Basically, the theory replaces this kind of forces by geometrical expressions called "constraints", which are relations between coordinates or/and velocities that can be determined by the geometry of the situation. This greatly simplifies the problem by reducing the number of coordinates or degrees of freedom.
It's quite cool of a method actually! I used this once to figure out time period for a simple pendulum and it was an Eureka moment when I actually got the familiar equation. Thanks Nick for the video, it's been a recap!
Learned this this semester in my theoretical physics course and while I appreciate the mathematical explanation I thought it really lacked the visual image of what's happening. This is why we have youtube and amazing youtubers like you. Thanks for the help!
The number of RU-vid views goes with the spectacularity of a video, not because of its genius content. And often goes for gossip or near-libel. Some truly informative YT channels spend an insane amount of money just to add some spectacle to the information they deliver. It is funny to my eyes, but necessary for many others. And yes, many people learn things by accident. And they forget them by rule. A sad business model...
2:40 There's this farmer, and he has these chickens, but they won't lay any eggs. So, he calls a physicist to help. The physicist then does some calculations, and he says, um, I have a solution, but it only works with spherical chickens in a vacuum.
Anuj Arora that is a great joke. It’s funny, and it makes you think. But also it doesn’t make you actually laugh out loud so no one thinks you’re a freak
@N/A ...What? Why does the scientist turn into multiple scientists on the 4th line? Why do these multiple scientists say "Pulls chicken closer"? Why am I wasting my time scrutinizing the grammar of a crappy worthless comment? Forget this, I'm gonna do my work.
Great video! The principle of least action pops up all over the place, I will be sharing this with my family. We're very lucky that you decided to make RU-vid videos.
I really enjoy watching your videos man. They are so easy to understand, even though the subject seems hard at first sight. You are doing a good job. Greetings from a 2nd semester student in Heidelberg. 🙋🏽♂️
This was great! I'm close to wrapping up intro mechanics, which is most definitely all about forces (Euler-Cromer anyone?). It's been loads of fun. Mechanics is a really interesting subject in general, and I'm really keen to see it from different points of view... Lagrange and Hamilton. So yeah, definitely do a video or two on Hamilton's work. Maybe even use Lagrange or Hamilton's technique to solve a "classic" problem that highlights the strength of the approach. Or whatever. Love the channel and thanks for taking the time to share your knowledge.
I totally get the idea, thank you. As a mechanical engineer (MSc) I think we learned the method as the "principle of lower energy" rather than "Lagrangian mechanics". We write the energy equations and try to find the lowest points, in most cases it leads to differential equations too complex to solve.
Bro , when I saw your video for the first time , I thought that may be it was a very famous channel and had millions of subs , just I was too late to notice it . But when saw your subs I was literally shocked . What the quality of your content needs at least 10 million subs .
I was literally reading about this today at work and I have a much better understanding of it now after having seen this. I’ve been thinking about taking a classical mechanics course at college, but it’s not really a chemical engineering thing haha. I feel like I might do it now just for fun 😝 Thanks
The more I watch your videos the more I know how little I understand any of these concepts. Yet, I still like them and enjoy your way of explaining in an entertaining manner!
I was introduced to your channel today, and I have watched several videos in a row. It's amazing, I haven't felt the same way since I watched Bill Nye the Science Guy as a little kid. You have so much enthusiasm for this, you're willing to fool around and make little jokes, but it adds so much to it that overly serious channels just can't compete with. You have a great understanding of how to communicate complex ideas in a simple way, and you seem to be having quite a bit of fun doing it. It's infectious! Keep up the good work, and stay crazy!
Nick, you have the BEST analogies in the whole Scientific universe. Your presentations are 100000 times more accessible to me than Feynman's (supposedly "easy") lectures. Sure, the visuals help, but it is fairly obvious to me that you have an AMAZING ability to pass on knowledge in the most "common sensical" ways. :)
i spent 30 years in college studying science. I thought i was quite good at it. my young niece who was getting her degree in physics brought home a book that was new to me: "Classical Dynamics" which had this topic covered. What a delightful surprise! By the way, while your videos are not as technical as some of the others they are fun to watch and I do pick up 'stuff' by watching them...thanks
Wow, Beautiful stuff! The shortest path is sometimes longer. I got my AA degree from Pasadena City College, I can’t tell you how many courses I took over and over. I came back to school years later and got my BFA in painting. A lot is going on and the shortest path is twisted and curved can’t begin to tell you what a strange World it is we live in. Math and Science is Beautiful.
Lagrangian concepts are not only applicable to mechanics, It applies to any pair of magnitudes that are tied in a similar way to that of energy and work. It can be applied to optimization problems where you can put the restrictions and the function to be optimized in the same equation. Langrange, this guy really blew up the whole thing!!!
Idk why but I like to think of Lagrangian vs Hamiltonion mechanics to be like Minecraft speedruns. Lagrangian is a set seed speedrun, where you know everything and you mathematically minimise your path through the world, while random seed speedruns are based on what information you have at the moment, and making decisions based on the current frame of the game.
Just watched several lectures on yt from a university classical mechanics course. Mostly listened to chalk on the board. This video has a denser amount of information in it. Bravo!
Good start, but you barely scratched the surface. An another more in-depth video would really help, especially for understanding the whole configuration space thing.
Alongside with quantum mechanics, Lagrangian mechanics is definitely the topic I had the most fun learning. It's also way less abstract than QM so I could just sit back and enjoy lectures at the uni. Beautiful times
@08:00 You have here, just provided an enlightened intuition of "action". I never thought about it this way but I like your description of action as the amount of *"VARIATION"* between KE and PE (along the path being considered); hence L = T *MINUS* V
OMG!!! Super!! Never seen ANYTHING more complete and clearer!!! Thank you so much!!! I met lagrangian transformations somewhere in my past university courses... a deep mistery ! 😳😱😱
Unlike many of the other RU-vid programs on physics, your audio quality and levels are consistent and clear throughout your program series, making your content much easier to follow and to understand. Your enthusiasm helps as well on that account.
The problem for most of us is: "Why choose action?" It is almost a fantasy quatity. In what other context do we come across action? I suppose that the fact that kinetic and potential energy were still incompletely understood in Lagrange's day allowed him the freedom to choose an absurd concept: "action". He got lucky. It worked. But for me, it makes no more sense than if he had started with his own inside leg measurement.
5:20 "Yes, this a math thing." I can hear the frustration in your voice. I'm guessing a lot of your students at the college got frustrated with the math? In your newer videos, since you've switched to youtube full-time you've been much enthusiastic about the math, which lots of people seem to like, myself included. It's awesome that you're able to teach the topics you want to teach, the way you wanna teach them and have people watch the videos because we _want_ to. It's so much more enjoyable teaching people who _want_ to learn.
I never thought about modeling degrees of freedom as a cartesian axis. That's nifty. I have to think about that more. I pick up so much from these videos that aren't even the focal points. So awesome.
Yep! In fact, the path the red dot takes at 7:12 is the path we're _actually_ using in the principle of stationary action. Lagrangian mechanics is done in configuration space.
You are the best physic youtuber toegether with PBS spacetime. There PBS has more complex and general topics you go and tell people to look on things more differently. Keep on going pls.
3:02 Contrary to popular belief, Fermat's Principle does not say that light will always take the minimum time path, it says it will take a path where the "first order variation" (ie, first derivative) is zero. Grad students in seismology get this pounded into them because there are cases where the travel time is a maximum, not a minimum. That would be a good topic for a followup video.
Wow great video Nick!!👏👏 You explained it in an unprecedented way. And I am wondering on the fact that on the macroscopic levels how these two phenomenons, law of least action and law of thermal equilibrium respectively which seems to be the fundamental in nature, are just the result of the more preferred event of Quantum mechanics where these laws can also break but rarely. What you think about it??
Let's get 'The Science Asylum' to a million subscribers 🙂 Relevance of any topic or idea in Science is important and this installment by Nick addresses the relevance of Lagrangian mechanics vs the giant 'Newtonian mechanics'. I have watched all videos on this topic and without any bias, I vote this one as the best 🙂 Thanks Nick and keep it up ❤ On a side note, Nick can you throw some light on how you animated the double pendulum @ 2:00 (only if it's not a problem)
As usual. Fantastic content. However, I must point out that the content leaves the viewer a little bit less crazy after viewing than before viewing. Is this part of the master plan? Ha! Just kidding, of course. Thank you for all you do!
Path integrals are so intuitive (conceptually) thanks to lagrangians. You have an infinite number of paths that can contribute to an amplitude, but the only ones which minimize the action really contribute since it's proportional to e^{-S} (in imaginary time)
Awesome video. You reminded me my studies in the university of Athens, years ago. Learning lagransian/Hamiltonian mechanics (along with Noether theorem, of course )was one of the most mind-blowing things that happened to me. I can compare the feeling with the one when I leart about Incompleteness theorems, quantum mechanics, or the theory of evolution. Thanks a LOT for you great work! PS: A video about Noethers theorems on symetries would be a great idea, I think :)
I did a video on the history of Noether's theorem a while ago: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ahf0zCaqrwM.html but I'm hoping to go into more detail soon.
Wow. Lagrangian mechanics is so cool. I think it's mentioned in my analytical mechanics course which is the next semester. I now at least have an idea of what it is before I deal with it. You teach very complicated stuff so easily and your way of animating stuff helps a lot to visualize things.
Thank you! I seriously appreciate the way you explain things while emphasizing that it's a model or way of thinking about things. Other explanations that seem to invoke some metaphysical interpretation of reality just make the raw _thing_ more difficult for me to understand.
THIS IS THE BEST TUTORIAL I HAVE EVER SEEN IN MY WHOLE LIFE MAN U ROCK YOU DONT BELONG TO A AN ASYLUM YOU ARE A GENIUS . CRYSTAL CLEAR EXPLANATION ON LAGRANGIAN MECHANICS
Brief but accurate and informative video on the Lagrangian and the principle of least action. It does a better job than most popular science texts and even textbooks in exposing the essentials. 👍👏
Amazing channel, I'm glad I found this channel that covers many questions that people have, and breaks everything down into the very basics. Keep the videos coming!
Hiy nick your type of explaination is so very understanding and so nice and i liked it well you . I have a small doubt if black holes are explained by swarchild radius can every matter turned into black hole ...
@@ScienceAsylum I disagree. Objects with rest mass lower than planck mass can't turn into black holes, because they don't fit within their own Schwartzshild radius.
From what I understand, Lagrange based his mechanics on an idea from d'Alembert about virtual work. The principal of virtual work is another time-saving physics concept which gets messed up too; I'd be interested on your take on that one (not that you're not busy or anything).
I liked the visual aid of assigning a Lagrangian value to every point in space, and then the correct path is the one whose sum of values it hits is least. It's not intuitive that kinetic energy is a function of position. But a conservative force's potential energy is a function of position, and total energy is conserved. So given one value of kinetic energy, you'd be able to assign a value of L to every point in space.
Love your videos! However, the proper way to define the Lagrangian is using the kinetic co-energy (instead of the kinetic energy, as is stated in the video), because for the Lagrangian the configuration space is the tangent bundle (instead of the cotangent bundle; some nice confusing vice versa naming to create some extra fun). Or put in other words: L(q,q̇) = T*(q̇) - V(q). Where L is the Lagrangian as a function of the generalised displacements (q) and the time derivative of q (q̇, which is also called flow); T*(q̇) is the kinetic co-energy as a function of q̇; V is the potential energy as a function of q. We need to define L using T*, because the kinetic energy (T) is not a function of the flow (q̇), but of the generalised momentum (p): T(p) = p * q̇ - T*(q̇). From which it follows that T(p) and T*(q̇) are only equivalent (i.e., T(p) = T*(q̇)) in the case that there exists a linear relation between p and q̇. Which of course is often true with the relation between momentum (p) and velocity (v) (where x is the displacement) p = m * ẋ = m * v, but not in general.
And not only classical. Quantum field theory relies on the quantization of "field" lagrangians. That means, also modern theory of physics uses lagrangian mechanics to arrive important results :D
He can't because it is... It has been measured and proven true - Stuff is pretty much empty space. If it wasn't most actions would be Impossible for example: Chemistry!
Maybe krishna CoC meant that we should consider the fact that there is no such thing as empty space, even in a perfect vacuum there is still a quantum field that ripples and undulates. But yes if we exclude fields and specify that we are only considering matter, then atoms are something like ~99.9% empty space. But by excluding fields we might be doing something very strange, perhaps matter can't even exist without fields.
@@capnbilll2913 if you say the Protons and Neutrons have mass (and we all agree it's minute) then you must conceed that the Atom cannot be 100% empty space.
Ha! I just finished a statistics class and programmed a bunch of algorithms using degrees of freedom in excel. This video helped explain why that data point matters. Bonus points on the fireworks!!
