Hidden Geometry of the Pendulum

[@isaackay5887]

I found elements of Calculus 1-3, Diff. Eq., Nonlinear Dynamical Systems, Mathematical Modeling (dimensional analysis), and a hint of Scientific Computing (error analysis)...all incorporated into one concise, easy-to-understand video in 10 minutes or less. Bravo and well done!!

[@kwenatoor1765]

Hahaha thank you so much!! This comment made me happy. A little taste of everything, to see how they all come together to help us understand and model the world :)

[@josecolmenarez7003]

“Fundamental theory of engineering” That killed me HAHA

[@kwenatoor1765]

LOL it appeared for a split second but im glad you caught it

[@darinpringle5611]

5:35

[@JohnDlugosz]

I like how your _algebra ballet_ is more reminiscent of the original animations by James Blinn, in contrast to how 3b1b's code just morphs the text much of the time. The hand-drawn graphics give a nice feel to it. I hope you figure out how to combine the hand-drawn elements (drawn only once) with computers to do the actual animation, programmatically moving those elements around.

[@kwenatoor1765]

I really really like this comment! It would be a fantastic feat to be able to do this type of animation programmatically, hopefully then extending the style to even more complex scenarios with ease. I like the idea of it having a handwritten feel, like I'm writing each line and letter on paper, but then they come alive and dance and move on the paper. Algebra ballet is a beautiful way of putting that feeling into words- thank you for that imagery

[@JohnDlugosz]

@@kwenatoor1765 If you're not familiar with it, look up _The Mechanical Universe_ . The Wikipedia article has a reference to its official home website where you can stream all the episodes for free. I was fortunate enough to see James Blinn speak (and then went out to eat with him!) in the early '90's. I'll reply more later about some thoughts on how you could make the animation more programmatic. Maybe we can get in touch in a more suitable discussion forum.

[@MrRyanroberson1]

and here I thought there was already a math library for vector-animating hand-drawing as long as you lay out the path... i'd have to go looking for a long while to find the video for it again, though

[@CanalBrunoP]

@@JohnDlugosz Could you tell us which forum you find discussions about making programmatic animations you mentioned? I'm interested in learning, but I don't know which tool to start with

[@robertschumann6977]

Really like your style of animation (don‘t want to imagine the effort). Also, your video has a very relaxed atmosphere. Keep up the great work (even if only once in a few months)!

[@kwenatoor1765]

Thank you :) i have an idea for the next video actually- and that comment about keeping it up even if rarely really made my day, I appreciate it!

[@cellobuilder]

I’m interested in seeing more of this content. (And composing for it if that’s okay with you too)

[@radiradev3013]

I loved the energy approach to the solution! Beautifully animated and narrated!

[@NathanGamingTube]

Loved this! This video encompasses my nerdy brainwaves as I try to go to sleep, and sums up a lot of relevant maths I'd encounter daily! Good job

[@michaelquinlan9594]

Javier!!! Well done. Clear explanation and beautiful graphics. Oh, and your voice...so soothing to listen to.

[@Higgsinophysics]

Epic and unique style.. awesome job

[@brickie9816]

Wow is this your first video? Very impressive. I really liked how everything was laid out, and i love that i dont need to ask for music title because i would totally do that ;) you earned yet another sub

[@kwenatoor1765]

Thank you for the kind words! Happy to have you here :)

[@royalninja2823]

That was delightful to watch, all the little animations and edits were incredibly charming and you conveyed the information very well. Great work!

[@BurkeMcCabe]

This is so awesome! The visualization of the 3d growing and shrinking circles that intersected at a place👌

[@sokka90ml]

That's why modifying and reconstructing string theory for higher dimensions is interestingly better way to approach gravity

[@waso_laso_sewi]

This is very good, I love the music, the animation, the way you explain the Physics, all of this! I would absolutely love to see more!

[@adamb7088]

Really nice video and I look forward to any videos my might produce regarding Fourier and Complex analysis. Thanks.👍

[@exandra.]

I loved this! I'm taking an IB physics HL course and it discusses this topic, but in less detail, this was fascinating to watch as it unveiled some of the mechanisms behind the stuff I'm studying, even if I don't grasp all of the calc yet lmao

[@MCSteve_]

Idk your situation but that does not stop me to share my experience. Lmao. Stay strong! IB is definitely rigorous but it is an amazing opportunity. Good luck on your Papers, IA's, EE... :)

[@exandra.]

@@MCSteve_ Thanks, I'm finishing up my Physics EE right now, it was quite fun in all honesty :)

[@menturinai1387]

This is a really great presentation on the solution of a pendulum system, with a good mix of quick "just plot it" approach as well as a mathematical derivation! I also love the style of the video. Keep it up!

[@kwenatoor1765]

Thank you! I’m glad both perspectives felt complementary. I hope to make another video eventuallt when I have time :)

[@Simeulf]

A genius made this video. Simplicity is genius. Please post more videos.

[@mavlonkarlsefni]

Wow! It's my first time seeing hand drawn pictures in physics video. Very cool idea! Also I like your style, it is so pleasent to watch, man! Greetings from Russia, keep up the good work brother

[@mavlonkarlsefni]

But there is some pictures, that are appearing for 0.1 second, and I can't understand what is this, so please, leave them on the screen for a longer period of time!

[@khaledel-sisy3203]

That was incredibly amazing, extremely high quality content! ❤️❤️❤️ Please do more of these videos, I am waiting for more.

[@thebees955]

Enjoyed this a lot - loved your animations, especially the bit about level sets!

[@kwenatoor1765]

Thank you! I personally love this visualization of how level sets connect the concept of energy to the allowed solution curves -- I just had to include it! I would have liked to see this visualization in more of my physics courses

[@Darakkis]

This is it! Amazing work, i wish you did more

[@quantumobject3815]

I love these animations Keep up that great work

[@colinthomasson3948]

Enjoyed this, particularly the way the 'more rigerous approach' starts off from another approximation. But with added mathematical analysis. Making it thoroughly respectable, in a rigerously mathematical sort of way

[@alexandre3388]

Woah that’s amazing, looking forward to uni so that I too can do stuff like this !!!

[@mastershooter64]

Quite a fun video! I'm actually doing this exact same thing right now as I'm going through Taylor's classical mechanics, using the energy formalism to derive the equations of motion for various physical systems, like the pendulum, atwood machine and this weird metal ball on a vertical wire attached to a block through a pulley lol I loved how you make a connection between geometry and the actual system! I know about phase spaces but I never thought of them as the level sets of the total energy of the system! As a geometry enthusiast I am a bit vexed about not thinking about actually plotting the total energy as a function of position and velocity D: but you live and you learn! I quite like this style of animation, I would like to make videos of a similar style.

[@benheideveld4617]

Please use a disk with an eccentric mass, such that the pendulum can fly over the top. Adding linear friction becomes easy by positioning two magnets on both sides of the disk. Now add a linear motor to make it into a damped driven pendulum. The simplest chaotic system from classical mechanics. You get a strange attractor in phase space.

[@questionablemathematician3902]

well done video, friend :)

[@AbelShields]

I love that the plot of the level sets shows solutions where you give it enough kinetic energy to swing right around and keep on going, increasing theta indefinitely 😍

[@tommysiegel9295]

wonderful, beautiful & powerful

[@Posesso]

Even if I knew most of was being told, I enjoyed this a lot. The drawings and colors are neat, I like the animations a lot, that background music (!), and well, I love how you solved the differential equation. It's always satisfying to see it and not everybody goes step by step. I like how you substitute numbers in equations to simplify. I don't what I like so much, maybe it's not as fast as other videos I watch. For me, just the volume was very low.

[@kwenatoor1765]

Right! I think there is value in explicitly showing how the equation slowly evolves to the final answer step by step, and i’m happy the speed was appropriate. I wanted to go at a gentle pace and not rush it. I agree about the sound thing, I will try to amplify it and speak up next time. Thank you for the comment!

[@Posesso]

@@kwenatoor1765 ❤️🦩

[@marcopivetta7796]

hey! this is pretty cool and easy to understand! wish i knew about this video when i started reading Kelso's Dynamic Patterns (great book, btw)

[@KineHjeldnes]

Yes, please do more of this. :)

[@mindsetrader]

This is taught in 12th standard in Indian Schools🙂🙂 I too learnt it in my 12th standard but from your video I got a deeper understanding of the working of the formulas. Thanks again🙃👍

[@kwenatoor1765]

Oooh I see! Happy you found it useful, cheers 😃

[@thomas_delaney]

Well produced video, keep it up.

[@maxwellsequation4887]

Rigor fine print was good

[@YashwanthXtreme]

Really loved the animation, the content, the depth of math could be a little more but over all the best video for visual learning ❤

[@adelmomorrison3517]

Lovely style

[@averagecornenjoyer6348]

simply, amazing. I absolutely loved this video.

[@sirgae5113]

That was a really nice video, the animations and your explanations were nice too.

[@modeler4]

Like others have said, good balance of graphics and math, hope you can find that 80/20 solution!

[@Statevector]

Excellent! Subscribed!

[@joaofrancisco8864]

Great video! I really hope you intend on making more.

[@Pengochan]

This approximation is why the pendulum in pendulum clocks ideally should have only small deflections from the vertical.

[@Anne_Ony_Mouse]

Larger deflections are still periodic. They just don't fit a perfect sine wave.

[@Pengochan]

@@Anne_Ony_Mouse they have a different time period, and that change increases the bigger the amplitude.

[@jonathasdavid9902]

I just love your video!

[@B_R_U_N_0]

good video. good initiative... keep going brother

[@subtlethingsinlife]

Oh it is your first video .... That's awesome ..... please please upload more videos of complex mathematics and physics concepts such as electrical circuits, waves, thermodynamics

[@elena6516]

There are thousands of those videos already - look up "Physics Videos by Eugene Khutoryansky"

[@kwenatoor1765]

Yes I plan to! Stay tuned

[@hisoka4027]

very nice video, please make more of these

[@denysolleik9896]

I wish I could understand this, wizardry.

[@physira7551]

this is very beautiful

[@Serghey_83]

E(θ, θ') = ½m(lθ')² - mgl·cos(θ) In general: F(x, y) = a·y² - b·cos(x) where a,b - constants

[@chemsdinesidha5254]

Magnifique vraiment... Merci.

[@sobreaver]

Interesting approach

[@isaacstamper7798]

Subscribed

[@elena6516]

58 seconds in and wonderfully impressed! Perhaps you can cover a problem related to this one, but is too complex for my level of calculus understanding. Could you calculate the tangential velocity of the outermost pendulum bob in a double pendulum system as a function of the tangential velocity or acceleration of the inner pendulum bob?

[@kwenatoor1765]

That's funny - I've been pondering over the double pendulum for a couple days now LOL so good timing. Finding that it's quite a complicated thing. I want to do a proper treatment of these coupled oscillator type of systems, but it may be a while till I have a good break to work on that. Stay tuned though and thanks for the comment :)

[@AliVeli-gr4fb]

very nice, thank you

[@TheDummbob]

Nice Video man, inspiring to think about klassical dynamical laws as artifacts of the geometry of phasespace... I wonder how it translates to quantum mechanics Especially since, from what i've gathered, this more abstract point of view on classical mechanics culminated in Hamilton Jacobi theory inspiring schrödinger to write down his famous equation

[@kwenatoor1765]

Now that makes my bones vibrate- a video diving into some visualizations of quantum mechanics would be incredible. When I was first learning about the idea of a wave function and the Schrodinger equation, I would have loved to spend some time thinking about what they mean, how we should interpret them, etc. Sadly my QM class ended up being nothing more than doing ton of integrals and never diving into WHY we were doing them!

[@TheDummbob]

@@kwenatoor1765 Yes! I guess that is the fate of most students of ohysics nowadays - "shut up and calculate!" But I think this is exactly *not* the kind of mentality that led Schrödinger, Heisenberg and co. to their incredible findings. Its a bit shit that the intuition behind the formulas is largely left untought in universities - gladly we live in the age of youtube, computer visualization and e-lerning :D I have hope that many many good videos explaining physics/math intuition will come in the future (no pressure haha)

[@mastershooter64]

@@kwenatoor1765 This is why you need Shankar my friend :)

[@Czeckie]

those animations are superb!

[@patrick-kees8962]

Can't wait for the next video

[@HardFlip310]

Great job 👏

[@danneil8778]

excellent mood, very easy to follow, thanks.

[@Mike.G97]

Great video! 🎉

[@eulertoiler9774]

well done!

[@cjhapich2224]

great video!

[@viniciusfriasaleite8016]

Really cool video!!!

[@eqwerewrqwerqre]

The info cutaways should last longer. I desperately want to read it but i simply cannot get it to pause there on my phone

[@blusham4629]

This was great

[@rommathedex_657]

I just struck a gold mine of content

[@kwenatoor1765]

hahahaha that makes me happy. I already have one good idea for a continuation to this... maybe I should do it

[@b_phatt]

i like this... animation so good...

[@idirkhial9422]

Great Video! Hope we get to see more.

[@TranquilSeaOfMath]

Nice animations and lesson.

[@BorisNVM]

really cool

[@PianoBounty]

Is this what people call ASMR?

[@oscarstaszky1960]

brah how did ya even manage to use Langrangian Mechanics without even saying its name in the first place AHAHAHAHAHAHAH anyways this is still a wonderful video man more power to ya

[@kwenatoor1765]

LOLLLLLLL it's just i havent formally educated myself on Lagrangian mechanics yet so i didnt wanna overstep and make some wrong statements abt something i dont know too well hahahaha

[@maxwellsequation4887]

@@kwenatoor1765 lol

[@strengthman600]

Nice

[@reyuniorv6005]

Amazing

[@rv706]

Well done!

[@01k]

Good stuff

[@Anonymous-kj6cu]

Love how you put music flowing in background. Name of the music?

[@matthewjames7513]

loved the animation!! Can you elaborate more on how you hand-animated it?

[@kwenatoor1765]

thank you! I did this using the Flipaclip app for ipad. Not a very high level tool but it works for this purpose. In flipaclip, you need to draw each frame in the animation, but there are ways to speed up the process using copy& paste moving things around, etc particularly because most of the objects in this video are simple geometric shapes and lines

[@ishikani]

Feels like I'm watching an episode of Monogatari but I can understand it more than 10%

[@Ricocossa1]

Don't you insult my favorite show now.

[@almasrafi4102]

Nice explanation....

[@marcelotosin5670]

Soooooo cooollll

[@TheJara123]

Wel done, I am making videos with this kind of animation, simple and beautiful.

[@johanngambolputty5351]

Very nice! What happens if you take a higher constant total energy, do you get different motion from those weirder level sets? I'm guessing that's the angle going over pi? You even get straight lines in theta at what I'm guessing is the pendulum balancing on top :)

[@kwenatoor1765]

Great point! Yes totally, if you begin with our approximate circle path, then going higher up the level sets you get first some more ellipse-like shapes, and then at one key point you break free from a closed loop path into a weird squiggle and then an almost line. You could imagine a very high energy pendulum literally swinging around and around the pivot like swinging a ball on a string, with immense speed. Not much of a pendulum at that point. But it’s interesting to think about the limit cases isn’t it? :D

[@williamworthy4091]

great vid

[@Pedritox0953]

Wonderful video!

[@MACaronyboy]

for the kinetic energy, should you also factor the contributing of the rotational inertia?

[@brianhu6277]

Please make more!!

[@gabitheancient7664]

cool video

[@shambosaha9727]

Fantastic

[@mericinhikayesi8474]

There are a formula Between the 3.31 - 3.32 minutes

[@nazishahmad1337]

Can you tell me how do you create your videos .

[@lucasalland9547]

at 4:52, why do you choose to set the right term equal to zero and not the left term? What would be the interpretation of either way?

[@kwenatoor1765]

Good point! The left term set to zero would be: ml dθ/dt = 0 Which has a solution: θ = a constant. This is the solution where the pendulum stays still for all time, which I think intuitively we know it is possible, if it hangs straight down motionless, but that's not very enlightening. Ultimately, that left term gives a physical but so-called "trivial" or obvious solution, while the right one gives a more interesting solution we didn't already know.

[@MarcDufresneosorusrex]

would you say the formula that undergirds Physics is the idea of PE potntial energy?

[@bramburka018]

could someone tell me how do you graph such formula? and get the result in 3D

[@BarkanUgurlu]

Use Jacobi elliptic functions dude. Animations were nice tho

[@mrce2000]

Great Video

[@therealist9052]

Tell me you're doing Lagrangian mechanics without telling me you're doing Lagrangian mechanics lol.

[@user-sv5vb1mj1q]

I do not understand scenario when pendulum has high speed. According to logic, is should spin in circles, but according your energy plot geodesic plots it will spin just half of circle?

[@kwenatoor1765]

You’re right, above a certain speed, it should just spin in circles. The plot in the video is only an illustration of a small section i chose to focus on. There is more that was just not included in the picture. If you extend out the plot out even larger you can find solution curves which are like a wiggly line. This corresponds to the pendulum spinning around and around forever just like you predict