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 - https://www.myphysicslab.com/pendulum...
2. Chaos GIF - Ari Rubinsztejn, CC BY-SA 4.0 https://creativecommons.org/licenses/..., via Wikimedia Commons


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1. The Simple Pendulum is not so Simple -    • Physics of the Simple Pendulum - Equations...  
2. The Chaos of the Double Pendulum -    • CHAOS of Double Pendulum (Lagrangian Analy...  
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PLAYLIST on Various Problems on MECHANICS
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*My Notes (PDF), and SCILAB Programs are uploaded to my PATREON, and Telegram Chanel*