Interactive Double Pendulum Periodicity Finder

This is a demonstration of interactively dropping a double pendulum at various points outlined on a heatmap, which shows the degree of chaos exhibited by the specific drop angle.

Features

• Lyapunov Exponent Heatmap: A heatmap that describes the sensitivity to initial conditions of each drop angle.
• Interactive Double Pendulum Simulation: Hover over points on the heatmap and see the corresponding animations.

Visual Demonstration

Installation

1. Clone the repository

2. Install the required packages:

   pip install -r requirements.txt

Usage

1. Run the main script to start the interactive simulation:

   python main.py

2. There will be a graph with an interactive heatmap of the Lyapunov exponents at different drop angles. Hover over them to see the exact angles and their corresponding Lyapunov exponents at the bottom right corner.

3. Press "u" to animate the corresponding double pendulum.

Files

• main.py: The main script to run the interactive simulation.
• 3d.py: A three-dimensional version of the heatmap.
• animation.py: Contains the methods to animate the double pendulum.
• data.csv: Contains the data of the Lyapunov exponents for different drop angles.
• requirements.txt: List of Python packages required for the project.
• lyapunov.pv: The logic behind calculating the Lyapunov exponents for each dropping point, written in python.
• README.md: This file.