The Chaos of Double Pendulum (Lagrangian Analysis | EOM | Simulation | CHAOS)

Using Lagrangian Mechanics to obtain the Equations of Motion of the Double Pendulum, and simulate its motion, as well as study CHAOS exhibited by the system.
Double Pendulum is a very simple construction using two pendulums attached to one another, free to oscillate. However, its motion is complicated to say the least. Its a good example of a chaotic system, which is very sensitive to initial conditions.
In this video I use Lagrangian formulation to obtain the Equations of motion of a Double Pendulum, and look at the solutions of the equations after numerically solving it via Scilab.
The results are incredible to watch!
Timestamps
00:00 Introduction
02:04 Obtaining the Lagrangian
15:02 Equations of motion using Euler Lagrange Equation
25:26 Numerical Solutions of the Equations
29:17 Results in SCILAB
34:30 CHAOS
38:45 Revision
Credits:
1. Simulation - www.myphysicslab.com/pendulum...
2. Chaos GIF - Ari Rubinsztejn, CC BY-SA 4.0 creativecommons.org/licenses/..., via Wikimedia Commons
Interested in moreeeeee....?
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1. The Simple Pendulum is not so Simple - • It's NOT so Simple: P...
2. The Chaos of the Double Pendulum - • The Chaos of Double Pe...
3. The Double Pendulum as Coupled Oscillator - • Double Pendulum as Cou...
4. The Coupled Pendulum (Normal Modes) - • The Love Affair of "Co...
5. Coupled Oscillators (Normal Modes/ Frequencies) • The Dance of Coupled O...
6. Damped Harmonic Oscillators - • The Physics of Damped ...
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8. BLOCK Stacking Problem (Very Interesting) - • How many Blocks can yo...
9. Terminal Velocity (Force Equations) - • Why Objects reach Term...
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11. Fermat's Principle to Snell's Law - • Fermat's Principle to ...
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PLAYLIST on Various Problems on MECHANICS
• Problems in Mechanics
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*My Notes (PDF), and SCILAB Programs are uploaded to my PATREON, and Telegram Chanel*

[@FortheLoveofPhysics]

Do you know that the double pendulum also behaves as a Coupled Oscillator for small angles? kzbin.info/www/bejne/Zqq0h2Siep2dr9U

[@muhammadazhar6708]

Sir which app you use for animation

[@physicschemistryandquantum810]

This channel is so underated

[@ShekharGupta-dh1iu]

Mind blowing stuff. Keep up the good work.

[@hazratyounaskhan4087]

Welcome back sir ! I was waiting for your new video.

[@jusemuan79]

Amazing, it's very clear the way that you explain, thanks 🙏

[@alert2084]

Sir you are great as you teach advance topics free💓💓💓💓💓💓💜💜💜💜💖💖💖

[@viggosimonsen]

Excellent presentation!

[@sauravveedu5667]

Thank you sir Please upload frequently

[@skshergill007]

Thanks.Very informative Sir. Your technique and representation of content is very impressive. Sir can you please tell me which software and tools you are using for recording this video?

[@pisicleclasses]

Great video sir... It will be cool to see the analysis of a perpetual motion machine.....

[@nacra2656]

Great Videod. Thank you!

[@vinayaktripathi8307]

This person is a genius.

[@NRUSINGHAPRASADMAHAPATRA]

Thanks sir 😊🙏🙏

[@debajyotibhattacharjee3180]

You are really very very good teacher ❤️❤️

[@anasfarid2492]

Hats off 🎩🎩

[@divyanshpatle7584]

Sir please make videos on atomic physics Your videos are just simply great!!

[@dryolymatics007]

Yeah what a great video. Thank you very much Prof. I was wondering if it will be possible to share your code. As tried using scilab to reproduce your plots and failed anyway.

[@jackiechan8703]

Sir it's was very impressive keep doing

[@avijitsen99]

Now, how are you sir? Is everything fine?

[@FortheLoveofPhysics]

I am Good now :)

[@Yps1249]

@@FortheLoveofPhysics sir ap itne din baad kyu sir.. Kya hua tha

[@harinachiappansubramanian9206]

Looks like my daily morning routine

[@octaviandatcu8677]

Great channel, it has a lot of potential. What do you use to create these videos? What tablet / software etc.?

[@FortheLoveofPhysics]

Wacom + OneNote

[@octavian_2]

@@FortheLoveofPhysics What wacom? :) You seem to write directly on a screen.

[@pauldirac6243]

Can you make a video showing us how the alternative to MATLAB's Simulink, Xcos, works in Scilab?

[@aravindhvenkatesan6480]

Thanks

[@nexaworldz]

d/dx cosx = -sin x During taking dot product of y1 and y2 sir

[@HimanshuSharma-xn6uc]

Make a video on Quantum physics related topics

[@pauldirac6243]

I typed in the code you displayed verbatim, and it doesn't run. It says, "ydash(2)= (1/((m1+m2)*l1-m2*l1*(cos(y(1)-y(3)))^2))*((-m2*l1*y(2)*y(2)*sin(y ^ Error: syntax error, unexpected end of line, expecting "," or )". I checked every parenthese 9 times, it's exact. Are you showing the same code that you ran for the graphs?

[@FortheLoveofPhysics]

shouldn't there be a parenthesis closure at the end, .. sin(y)

[@pauldirac6243]

​@@FortheLoveofPhysics I figured it out, thanks. The problem had nothing to do with that line, it was the next line where I had put ydash(3)=ydash(4) instead of ydash(3)=y(4). Unbelievable. I spent 4 hours troubleshooting that. The error messages they give you unfortunately can send you on a wild goose chase sometimes. Anyway, thanks for replying and for all the great videos!

[@zigzag_mode_on7140]

Can u tell me which software u have used for simulations?

[@natorgas]

At 23:40 : Why is the first term of dL/dTheta2 not negative? In the Lagrangian it's positive and because of the -sin it should be negative. Please explain.

[@mkjchannel8549]

Sir please upload videos on mathematics of general relativity

[@fatimayousaf5210]

Please make videos on electronics...

[@albinaruth9450]

Sir will you take classes for csir net physics exam

[@jhanolaer8286]

I try to make double pendulum simulation, but why it suddenly stop when i change timestep into .5 above?please help me

[@agnibhamajumdar9137]

Sir pls share how u programmed the pendulums

[@MrSadiq01]

Imagine if air resistance is addded to the differential equations how complex they will become.

[@anasahmad3859]

Sir please use board and chalk

[@mallaburhan7700]

Sir when will you start batch for iit jam 2022???

[@FortheLoveofPhysics]

May

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Will it be online and free for everyone ??

[@HimanshuSharma-xn6uc]

@@FortheLoveofPhysics how to join sir

[@phph9963]

Very good job Sr 👍 How I can contact u?

[@premsagar715]

Spherical Pendulum please!

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how could I find the programming?

[@Carlos_Eduardo_da_Silva_Lima]

+like please!.

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Qaqa ure ambilivibl