Double Pendulum

A Julia simulation of a chaotic double pendulum system using Lagrangian mechanics and RK4 numerical integration.

Initial parameters (angles, masses, velocities and lengths) are extracted from video analysis by tracking orange markers and fitting the simulation to observed motion.

Project Structure

│
├── bin/
│   └── main.jl                 # entry point
│
├── doc/                        # theory
│   ├── lagrange.pdf
│   └── lagrange.tex
│
├── export/                     # generated plots/animations
│
├── res/
│   └── video.mp4               # video to analyse
│
└── src/
    ├── Pendulum.jl             # main module
    ├── physics.jl              # physical constants
    ├── types.jl                # data structures
    ├── double_pendulum.jl      # simulation logic
    ├── video_analysis.jl       # video tracking & parameter extraction
    └── plot_manager.jl         # plot functions

Libraries

Simulation

• Plots.jl : visualization and animations
• DifferentialEquations.jl : ODE solver

Video Analysis

• OpenCV.jl : video processing
• Optim.jl : params estimation
• Statistics.jl : statistical functions

Development

• Revise.jl : hot-reloading during development

Measured Parameters

Physical Pendulum

• L1 = 91.74 mm
• L2 = 69.33 mm

Video (measured with Tracker)

• Ratio : 3840x2160
• Initial positions
  • Pivot : x = 1883, y = 933
  • m1 : x = 1872, y = 491
  • m2 : x = 1842, y = 175

Julia Setup

echo "Intall Julia 1.9.4"
juliaup add 1.9.4

echo "Set Julia 1.9.4 the default version for the current directory"
juliaup override set 1.9.4

echo "Launch the Julia REPL"
julia

echo "Open the package manager"
]

echo "Activate the local environment"
activate .

echo "Install and synchronize all dependencies"
instantiate

Run Simulation

Option 1: VSCode with Julia Extension

If you have VSCode with the Julia extension, go in bin/main.jl and press Option+Enter (macOS) or Alt+Enter (Windows/Linux) to run it directly in the REPL.

Option 2: Manual REPL

using Revise
using Pendulum
Pendulum.main()