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Physics Fluency
เข้าร่วมเมื่อ 14 ส.ค. 2021
Welcome to Physics Fluency, a channel dedicated to explanatory physics videos! I'm just a guy with a physics degree who really enjoys animating different physics concepts. I'm currently working on a video series on Lagrangian Mechanics, of which the first three parts are already available here on the channel. I also have many ideas for future videos about not just mechanics, but other cool stuff such as blackbody radiation ("the ultraviolet catastrophe") and visualizing crystal vibrations (phonons).
Lagrangian Mechanics III: Solving the cylindrical pendulum analytically #PaCE1 #SoME2
In this video, we solve a system of differential equations analytically through the means of linearization, and proceed to discuss the implications of the solution.
For the best viewing experience, make sure to watch in full-screen and 4K (2160p) resolution.
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This is an entry for a contest of Theories of Everything with Curt Jaimungal: th-cam.com/users/TheoriesOfEverything (specific video for the contest is th-cam.com/video/V93GQaDtv8w/w-d-xo.html)
This video is also my submission to the SoME2 event.
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Music in the background from www.fesliyanstudios.com
Blackboard image by Gerd 'geralt' Altmann: pixabay.com/sv/users/geralt-9301/
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#Physics #SoME2 #PaCE1 #Mechanics #Lagrangian #Pendulum
00:00 Intro
01:08 Linearization
03:36 Ansatz
05:17 Eigenfrequencies
09:55 Eigenvectors
11:27 General solution
12:16 Initial conditions
14:14 Recap
15:25 Showcase/Interpretation
19:30 Limiting case
20:50 Outro
For the best viewing experience, make sure to watch in full-screen and 4K (2160p) resolution.
------------------------------------------------
This is an entry for a contest of Theories of Everything with Curt Jaimungal: th-cam.com/users/TheoriesOfEverything (specific video for the contest is th-cam.com/video/V93GQaDtv8w/w-d-xo.html)
This video is also my submission to the SoME2 event.
------------------------------------------------
Music in the background from www.fesliyanstudios.com
Blackboard image by Gerd 'geralt' Altmann: pixabay.com/sv/users/geralt-9301/
------------------------------------------------
#Physics #SoME2 #PaCE1 #Mechanics #Lagrangian #Pendulum
00:00 Intro
01:08 Linearization
03:36 Ansatz
05:17 Eigenfrequencies
09:55 Eigenvectors
11:27 General solution
12:16 Initial conditions
14:14 Recap
15:25 Showcase/Interpretation
19:30 Limiting case
20:50 Outro
มุมมอง: 4 560
วีดีโอ
Lagrangian Mechanics II: Degrees of freedom, generalized coordinates and a cylinder
มุมมอง 10K2 ปีที่แล้ว
#Physics #Lagrangian #Mechanics Sorry about the wait! I hope the audio is bearable. The voiceover is by far the hardest part to get right and I'm still experimenting with how to make it better. I'm also hoping to be able to get a new mic soon. In this video, we introduce the ideas of degrees of freedom and generalized coordinates, before deriving equations of motion for a cylindrical pendulum. ...
Lagrangian Mechanics I: Introducing the fundamentals
มุมมอง 58K2 ปีที่แล้ว
In this video, we discover the classical Lagrangian, the principle of stationary action and the Euler-Lagrange equation. For the best viewing experience, make sure to watch in full-screen and with 4K (2160p) resolution. Music in the background from www.FesliyanStudios.com Blackboard image by Gerd 'geralt' Altmann at pixabay.com/sv/users/geralt-9301/ #Physics #Lagrangian #Mechanics
Amazing video, man! 👏
This series is great!! Did you stop making videos?
Amazing video! Thank you very much
these series on lagrangian mechanics are seriously the best videos on lagrangian mechanics I have ever seen! Funnily enough I live about 800 meters away from where Lagrange used to live here in Turin
Thank you so much for this work. ¿There is a bibliographic reference or an achademic resource that we can use to cite this proposal to understand Lagrangian? or ¿How can we cite your work?
Behavior of alpha, beta and gamma within a medium......
Him: "And that is how we found the Kinetic Energy by making many restrictions~" Me: "... That is one big equation for a super simple problem." Also, Amazing series btw. Can I ask how you create these beautiful animations? Thank you again!
Man you are great . your intuition is concrete. Thank you for sharing it
Why did we stop for tea?
The best Lagrangian video series I have seen.
But what is the delta δL means? 12:28
Wondering this as well, does it mean that the L function will always remain on the "L-axis"? There's two energy and one time direction in which the curve could be seemingly "perturbed"
PLEASE CONTINUE THE CHANNEL! YOUR WORK IS AMAZING, MAN.
Stupid musical background! How can one think adding noise enhances the signal?
Why cant we say dT or dV = 0 I guess because L contains both kinetic and potential energy so average height of curve is affected by each
You assumed potential and kinetic energies as vectors, but they are not. If they were, as you put it, the square of the total energy would be the sum of the squares of potential and kinetic energies, which we know is not true. Furthermore, even making this consideration, there would still be other errors. During your calculations, you assumed that the unit vector for L would be at -45°, which would only occur if kinetic and potential energies were always equal in magnitude all the time.
Since, as you say, energy is not a vector quantity, the vector sum in kinetic & potential phase space is not meaningful. 45⁰ line in phase space expresses the energy conservation constraint.
@14:24 I couldn’t visualize taking the signed integral of the L function and how it gives positive and negative areas wrt time axis. It looks all positive area
Excellent content. Hate the music.
For the rotational kinetic energy you used the moment of inertia about the cylinders center of mass. Why didn't you then apply parallel axis theorem to get the inertia about the pivot point? Since this cylinder is not rotating about its center of mass.
Good spot!
Due to the change in magnitude of the center of mass's location over time, inertia also changes over time
Im slightly confused as to what you are getting at. The center of mass location is dependent on time, but the magnitude of the center of mass itself is time independent, therefore the inertia about the center of mass is time independent. You may be thinking of the rotational kinetic energy term, which is time dependent due to the angular velocity component, theta dot squared. What I was pointing out was that in the video the author uses the center of mass inertia when building the lagrangian, but his object is rotating about a pivot point at the top of the cylinder, therefore he should have used parallel axis theorem to find the inertia about the pivot point.
great video by the way! Loved the animations@@jamesquigley4837
@@auden7560 you are right this cylinder rotates about the pivot point and this rotation is represented by using theta 1 but this cylinder also rotates with theta 2 and the rotational kinetic energy can be calculated using theta2. so using the center of mass inertia makes sense because of the change in angle theta2. You can't ignore the second theta because the system has 2 dof. Shortly, the Pivot point doesn't affect rotational velocity but the end of the spring ( top point of the cylinder) effects
I’ve never seen the idea L = T - V explained in any logical way. It makes the generalized coordinates make much better sense.
This is the ONLY explanation I've seen on TH-cam. I dont understand why others, including physics luminaries, just dump the formula on the screen and then explain algebra. This is BRILLIANT!
Agreed! I took high school physics 70 years ago, and the Newton was all we got. I've been figgering out this Lagrangian thingie bit by bit as I go along, but it's a huge relief to see it done simply and competently like this. Well done and thank you, Physics Fuency folks!
Wow that was mind blowing. Thank you for your work!
Such a satisfying payoff to visualize the eigendecomposition at the end!
What textbook did you use to learn the derivation of the Lagrangian Or did u figure it our yourself. Pls respond 🙏🏼.
What a deeper explanation in all 3 video on Classical Mechanics! Thank you sir to make Lagrangian approach a part of my understanding the Nature. Regards!
Thank you! I finished all three videos. The last one I had to rewind in a couple of places since there are quite a bit of calculations. These are by far the best series on Lagrangian Mechanics I can find on the internet. I understand this may be just a hobby project but the production is just unbelievable. Can't imagine how many hours you have put in creating these videos...
Beautiful, beautiful, beautiful! Thank you so much!!!
Extremely good description. I took "classical mechanics" last semester which actually just turned out to be an engineering dynamics course, so of course we didn't cover any of the interesting physics like gravitation into keplers laws, or lagrangian mechanics at all. We just did a bunch of stupid rube-goldberg math. Anyways, apart from that rant, now that the semester is over and grad school applications are all sent off I've been trying to teach myself the things I wasn't taught in class. I've acquired a couple classical mechanics textbooks, watched many videos, and this is the ONLY ONE that's ever motivated WHY the lagrangian is T-V. The energy space and allowed coordinates only being a single line, which can be represented by a single equation combining the two unit vectors is crazy. It make so much sense and only requires knowing you can make different coordinated spaces and knowing total energy is conserved! As well, I don't fully understand yet why the single trajectory restriction implies that the variation in the _time average_ of the lagrangian is 0. Shouldn't it just be the variation in the Lagrangian, or even just the integral of it over time? Why time average? Anyways, I've subscribed and will be watching this entire series. You have done amazing work here and I will be rewatching and taking notes on every video you make! I would love if you made more videos some day but definitely only do what you want to. Your passion for this material has made an incredible lecture and I'd be saddened to see another amazing creator run down by the algorithm. Thank you so much for your work, you have impressively contributed to the sum of human knowledge for all of us to enjoy. <3
Very great video 😊
Hey, where is the new one😢
He seems to have stopped. Paypal is also closed😢
It never made sense to me why L=T-V until I saw this video! this is the best explanation I've found!
We really Miss you sir 😢
May I ask if you know something? He seems to have stopped making videos and the paypal appears closed..😮
This is such a beautiful and unique explanation of Lagrangian mechanics. I am curious on how you thought up/discovered such an explanation and what you used to make the video
you gotta make more videos man.
As a 16 year old who got bored of ways of newton , this new approach for solving complex systems is like better
subbed
Amazing lectures. What software do you use to make these graphical geometries?
Nice that you have changed least action to stationary action...
Sir, this is a pristine video about a really hard topic in classical and quantum mechanics. Great great great! Thank you very much!
Ultraviolet catastrophe and about phonons are very pleasant to see yours vids on these.
Великолепно!!! Огромное вам спасибо! Вот бы аналогичное для гамильтониана!
Great video, wonderful explanations. 🎉
Until I watched this video, I knew why the derivative of the functional S with respect to epsilon should at 0 should be 0 and this improve me to understand more the Euler-Lagrang Equation, so thank you veryyyyyyyy much.
This is such a great video thank you !!
Helped me grasp what I couldn't in classroom. Thank you!
Flipping the potential energy axis in the 3D-view tied a knot in my brain.
Fantastic video. Thank you so much. At 19:48, roughly, you probably mean "integration by parts" .. would be systematic .. not trial and error.
I guess that might be a better word for it - though it for sure feels like trial and error a lot of the time (at least when I do it). ;)
Absolutely amazing!
Thanks... I couldn't find the next video which you stated about.
In qm, the Lagrangian is not the most probably trajectory, it's the average trajectory. If you have 50% chance of +1 and 50% chance of -1, average is 0 but you will never get 0.
Cool! Thank you!