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

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

Рет қаралды 20,292

Күн бұрын

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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7. What if you fell through a TUNNEL through Earth - • PHYSICS PROBLEM: What ...
8. BLOCK Stacking Problem (Very Interesting) - • How many Blocks can yo...
9. Terminal Velocity (Force Equations) - • Why Objects reach Term...
10. WELL OF DEATH - Physics Problem - • Well of Death - Mechan...
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*

Пікірлер: 51

@FortheLoveofPhysics 3 жыл бұрын

Do you know that the double pendulum also behaves as a Coupled Oscillator for small angles? kzfaq.info/get/bejne/Zt-BiZSdqp7Oqac.html

@muhammadazhar6708 Жыл бұрын

Sir which app you use for animation

@physicschemistryandquantum810 3 жыл бұрын

This channel is so underated

@ShekharGupta-dh1iu Ай бұрын

Mind blowing stuff. Keep up the good work.

@hazratyounaskhan4087 3 жыл бұрын

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

@jusemuan79 Жыл бұрын

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

@viggosimonsen 7 ай бұрын

Excellent presentation!

@nacra2656 4 ай бұрын

Great Videod. Thank you!

@sauravveedu5667 3 жыл бұрын

Thank you sir Please upload frequently

@pisicleclasses 3 жыл бұрын

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

@alert2084 3 жыл бұрын

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

@vinayaktripathi8307 2 жыл бұрын

This person is a genius.

@NRUSINGHAPRASADMAHAPATRA 3 жыл бұрын

Thanks sir 😊🙏🙏

@skshergill007 2 жыл бұрын

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?

@debajyotibhattacharjee3180 Жыл бұрын

You are really very very good teacher ❤️❤️

@jackiechan8703 3 жыл бұрын

Sir it's was very impressive keep doing

@divyanshpatle7584 3 жыл бұрын

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

@dryolymatics007 2 жыл бұрын

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.

@anasfarid2492 3 жыл бұрын

Hats off 🎩🎩

@aravindhvenkatesan6480 11 ай бұрын

Thanks

@pauldirac6243 Жыл бұрын

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

@harinachiappansubramanian9206 3 жыл бұрын

Looks like my daily morning routine

@octaviandatcu8677 3 жыл бұрын

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

@FortheLoveofPhysics 3 жыл бұрын

Wacom + OneNote

@octavian_2 3 жыл бұрын

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

@agnibhamajumdar9137 2 жыл бұрын

Sir pls share how u programmed the pendulums

@avijitsen99 3 жыл бұрын

Now, how are you sir? Is everything fine?

@FortheLoveofPhysics 3 жыл бұрын

I am Good now :)

@Yps1249 3 жыл бұрын

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

@zigzag_mode_on7140 2 жыл бұрын

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

@mkjchannel8549 3 жыл бұрын

Sir please upload videos on mathematics of general relativity

@HimanshuSharma-xn6uc 3 жыл бұрын

Make a video on Quantum physics related topics

@fatimayousaf5210 3 жыл бұрын

Please make videos on electronics...

@albinaruth9450 3 жыл бұрын

Sir will you take classes for csir net physics exam

@jhanolaer8286 3 жыл бұрын

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

@natorgas Жыл бұрын

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.

@nexaworldz 3 ай бұрын

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

@phph9963 3 жыл бұрын

Very good job Sr 👍 How I can contact u?

@anasahmad3859 3 жыл бұрын

Sir please use board and chalk

@fatmaalhashimi2023 5 ай бұрын

how could I find the programming?

@premsagar715 2 жыл бұрын

Spherical Pendulum please!

@mallaburhan7700 3 жыл бұрын

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

@FortheLoveofPhysics 3 жыл бұрын

May

@tamaldatta8520 3 жыл бұрын

Will it be online and free for everyone ??

@HimanshuSharma-xn6uc 3 жыл бұрын

@@FortheLoveofPhysics how to join sir

@MrSadiq01 6 ай бұрын

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

@pauldirac6243 Жыл бұрын

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 Жыл бұрын

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

@pauldirac6243 Жыл бұрын

@@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!