🌌 Double Pendulum Simulation (Glowscript)

Created by Maximillian DeMarr
Last major update: 2025-05-21

Interactive 3D simulation of a double pendulum built using GlowScript. This project simulates real-time motion based on Lagrangian mechanics and Euler integration.

🔗 Live Demo

👉 Click here to launch the simulation in your browser

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🎮 Instructions

• Click "Running" to pause or play the simulation.
• Use the Simulation Step dropdown to adjust precision (larger steps run faster, less accurately).
• Drag masses to reposition them manually (pause first for best results).
• Right-click + drag to rotate the view, and use your scroll wheel to zoom.
• Toggle Show Graphs for energy tracking (note: high detail may reduce performance).
• If motion becomes erratic, increase Damping or reload the page.

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📊 Physics Overview

The system is modeled using the Euler-Lagrange equations, with angular accelerations derived symbolically and solved numerically using the forward Euler method.

⚠️ This project defines positions in the following way. This is opposite to the conventional vertical orientation, due to how Glowscript handles axes.

$$x=\cos(\theta) \quad y=\sin(\theta)$$

🧮 Energy Equations

Kinetic Energy:

$$T = \frac{1}{2}m_1(\ell_1^2 \dot{\theta}_1^2) + \frac{1}{2}m_2\left(\ell_1^2 \dot{\theta}_1^2 + \ell_2^2 \dot{\theta}_2^2 + 2\ell_1\ell_2\dot{\theta}_1\dot{\theta}_2\cos\Delta\theta \right)$$

Potential Energy:

$$V = -m_1g\ell_1\cos\theta_1 - m_2g\left(\ell_1\cos\theta_1 + \ell_2\cos\theta_2 \right)$$

🔁 Angular Accelerations

$$\ddot{\theta}_1 = \frac{m_2g\sin\theta_2\cos\Delta\theta - m_2\ell_2\dot{\theta}_2^2\sin\Delta\theta - (m_1+m_2)g\sin\theta_1}{\ell_1(m_1 + m_2\sin^2\Delta\theta)}$$ $$\ddot{\theta}_2 = \frac{(m_1+m_2)(\ell_1\dot{\theta}_1^2\sin\Delta\theta - g\sin\theta_2 + g\sin\theta_1\cos\Delta\theta)} {\ell_2(m_1 + m_2\sin^2\Delta\theta)}$$

where

$$\Delta\theta = \theta_1 - \theta_2.$$

🧮 Related Tools

This repo uses:

• SymPy for symbolic derivation of motion equations → EOM Parser Repo
• GlowScript for 3D browser-based physics rendering

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🧑‍💻 Author

Maximillian DeMarr
Built with curiosity, calculus, and caffeine ☕.
For inquiries or collaborations, feel free to reach out!