Double pendulum · ling-3.0-flash
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.
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 with: 1. Correct equations of motion for a double pendulum 2. Canvas drawing of the arms 3. Colorful fading trail of the tip Let me write a complete HTML file with all CSS and JS inline. The double pendulum equations of motion: For a double pendulum with: - m1, m2: masses - L1, L2: lengths - θ1, θ2: angles from vertical - ω1, ω2: angular velocities The Lagrangian-derived equations are: (m1 + m2) * L1 * ω1' + m2 * L2 * ω2' * cos(θ1 - θ2) + m2 * L2 * ω2² * sin(θ1 - θ2) + (m1 + m2) * g * sin(θ1) = 0 m2 * L2 * ω2' + m2 * L1 * ω1' * cos(θ1 - θ2) - m2 * L1 * ω1² * sin(θ1 - θ2) + m2 * g * sin(θ2) = 0 Solving for ω1' and ω2': Let Δ = θ1 - θ2 ω1' = [ -g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2*sin(Δ)*m2*(ω2²*L2 + ω1²*L1*cos(Δ)) ] / [ L1*(2m1+m2 - m2*cos(2Δ)) ] ω2' = [ 2*sin(Δ)*(ω1²*L1*(m1+m2) + g*(m1+m2)*cos(θ1) + ω2²*L2*m2*cos(Δ)) ] / [ L2*(2m1+m2 - m2*cos(2Δ)) ] I'll implement this with RK4 integration for accuracy, draw the pendulum arms, and create a colorful fading trail using HSL colors that shift over time. Let me write the complete file.
/tmp/ws/index.html (9854 bytes)Successfully wrote 9854 bytes to /tmp/ws/index.html
thinking
The file has been written. Let me verify it exists and check its size to make sure it's complete.
{"command":"wc -l /tmp/ws/index.html && head -3 /tmp/ws/index.html && echo \"---\" && tail -3 /tmp/ws/index.html"}342 /tmp/ws/index.html <!DOCTYPE html> <html lang="en"> <head> --- </script> </body> </html>
thinking
The file has been written successfully. It's a complete self-contained HTML file with: 1. **Correct double pendulum equations of motion** - Lagrangian-derived equations for two equal masses and equal lengths, integrated using RK4 (4th-order Runge-Kutta) for numerical accuracy. 2. **Canvas drawing** - The arms are drawn as lines with colored joints, and the tip has a glowing effect. 3. **Colorful fading trail** - The trail uses HSL colors that shift over time (hue cycling), with alpha fading based on age, creating a rainbow-like fading effect. 4. **Interactive controls** - Sliders for initial angles, length, mass, gravity, and trail length. Click on the canvas to reset angles based on click position. 5. **Info overlay** - Shows current angles and angular velocities. The file is complete and self-contained with no external dependencies.
The file is complete at `/tmp/ws/index.html` (342 lines, fully self-contained). **What's inside:** - **Correct Lagrangian equations of motion** for a double pendulum (equal masses & lengths), integrated with **RK4** (4th-order Runge-Kutta) for numerical stability. - **Colorful fading trail** — the tip's path is drawn with HSL colors that continuously shift hue over time, with opacity fading from bright to dim based on age, creating a rainbow-like comet tail. - **Interactive controls** — sliders for initial angles (θ₁, θ₂), arm length, mass, gravity, and trail length. Click anywhere on the canvas to reset the pendulum to that angle. - **Real-time info** — displays current angles and angular velocities. - **Dark theme** with glowing joints and a subtle radial glow at the tip mass. Just open `index.html` in any modern browser to see the chaotic motion unfold.
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
EVALUATION
Double pendulum simulation with colorful fading trail animates smoothly; click resets angles, drag/keys have little added effect.
Vision grade · anthropic/claude-sonnet-5
MEASUREMENTS
Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.