Maximizing Lyapunov Exponent in a Double Pendulum

Authors:

Joonhyun Chang, Justin Le
May 28th, 2024

Introduction

This project explores the chaotic motion of a double pendulum by calculating the Lyapunov exponent, which quantifies the system's unpredictability. The goal is to find the optimal initial angles that yield the highest Lyapunov exponent, indicating the most chaotic behavior.

Example Figure

Methodology

• Modeling the Double Pendulum: Derived equations of motion and simulated them using Euler’s method.
• Lyapunov Exponent Calculation: Simulated two states with a small perturbation to measure trajectory divergence and calculate the Lyapunov exponent.
• Parameter Optimization: Identified the initial angles that maximize chaos using a heatmap visualization.

Colab

Open in Colab