Double Pendulum - Derivation (Lagrangian Approach, Chaos & more)

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 Interested in moreeeeee....? ▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱ 1. The Simple Pendulum is not so Simple -    • Simple Pendulum (Step by Step DERIVATION)   2. The Chaos of the Double Pendulum -    • Double Pendulum - Derivation (Lagrangian A...   3. The Double Pendulum as Coupled Oscillator -    • Double Pendulum as Coupled Oscillator (Ste...   4. The Coupled Pendulum (Normal Modes) -    • Spring Coupled Pendulum - Normal Modes & F...   5. Coupled Oscillators (Normal Modes/ Frequencies)    • Coupled Oscillators | Normal Modes & Frequ...   6. Damped Harmonic Oscillators -    • Damped Harmonic Oscillations (Derivation )...   ▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱ 7. What if you fell through a TUNNEL through Earth -    • Motion through Earth (Tunnel) Derivation    8. BLOCK Stacking Problem (Very Interesting) -    • Block Stacking Problem (Step by Step)   9. Terminal Velocity (Force Equations) -    • Motion with Drag | Terminal Velocity (Step...   10. WELL OF DEATH - Physics Problem -    • Circular Motion - Mechanics Problem (Well ...   11. Fermat's Principle to Snell's Law -    • Fermat's Principle to Snell's Law (Derivat...   ▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱ PLAYLIST on Various Problems on MECHANICS    • Problems in Mechanics   ▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱ 💖Support   / dibyajyotidas   🌷 Donate https://paypal.me/FortheLoveofPhysics JOIN me on Telegram https://t.me/FortheLoveofPhysicsYT ▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱▱ *My Notes (PDF), and SCILAB Programs are uploaded to my PATREON, and Telegram Chanel*