Double pendulum · qwen3.5-122b-a10b
Output generated Cost / run $0.0092 Runtime 21.9s
Prompt for this run
Simulate a chaotic double pendulum on a canvas using the correct equations of motion, drawing the arms and a colorful fading trail of the tip.
TAKE IT TO CODE
A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.
RUN
METRICS
Transcript · 6 messages
Simulate a chaotic double pendulum on a canvas using the correct equations of motion, drawing the arms and a colorful fading trail of the tip.
thinking
The user wants me to create a single-page web app that simulates a chaotic double pendulum. This needs to be: 1. A self-contained index.html file with CSS in <style> and JS in <script> tags 2. No external resources or network requests 3. Uses the correct equations of motion for a double pendulum 4. Draws the two arms of the pendulum 5. Shows a colorful fading trail of the tip Let me write this simulation. The double pendulum equations are complex - I'll need to use numerical integration (like Runge-Kutta or Euler method) to solve them. Key components: - Canvas element for rendering - Double pendulum physics equations - Trail effect with color fading - Animation loop The equations of motion for a double pendulum are derived from Lagrangian mechanics. I'll implement them using the standard form.
index.html (8196 bytes)Successfully wrote 8196 bytes to index.html
thinking
I've created a complete double pendulum simulation in a single HTML file. Let me verify it was created correctly.
{"command":"ls -la index.html"}-rw-r--r--. 1 node node 8206 Aug 1 19:53 index.html
thinking
The file has been created successfully. Let me provide a summary of what I built.
Created `index.html` with a chaotic double pendulum simulation featuring: - **Correct equations of motion** - Uses the full Lagrangian-derived differential equations for a double pendulum - **RK4 integration** - 4th-order Runge-Kutta method for numerical stability and accuracy - **Visual elements**: - Two white arms connecting pivot → joint → bob - Colorful rainbow trail that fades over time (up to 1000 points) - Colored bobs at pivot, joint, and tip - **Interactive** - Click anywhere to reset with slightly randomized starting angles - **Real-time display** - Shows current angles in degrees The physics uses the standard double pendulum equations: ``` α₁ = [−g(2m₁+m₂)sinθ₁ − m₂g sin(θ₁−2θ₂) − 2sin(θ₁−θ₂)m₂(ω₂²l₂ + ω₁²l₁cos(θ₁−θ₂))] / [l₁(2m₁+m₂−m₂cos(2θ₁−2θ₂))] α₂ = [2sin(θ₁−θ₂)(ω₁²l₁(m₁+m₂) + g(m₁+m₂)cosθ₁ + ω₂²l₂m₂cos(θ₁−θ₂))] / [l₂(2m₁+m₂−m₂cos(2θ₁−2θ₂))] ``` Open `index.html` in a browser to see the chaotic motion!