Double pendulum · qwen3.5-plus-20260420
Output generated Cost / run $0.0093 Runtime 64.6s
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.
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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 a single-page HTML file that simulates a double pendulum with: 1. Correct equations of motion (Lagrangian mechanics) 2. Canvas rendering 3. Colorful fading trail of the tip Let me write this with proper physics. The double pendulum equations of motion from the Lagrangian are: θ1'' = (-g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2*sin(θ1-θ2)*m2*(θ2'^2*L2 + θ1'^2*L1*cos(θ1-θ2))) / (L1*(2m1+m2-m2*cos(2θ1-2θ2))) θ2'' = (2*sin(θ1-θ2)*(θ1'^2*L1*(m1+m2) + g*(m1+m2)*cos(θ1) + θ2'^2*L2*m2*cos(θ1-θ2))) / (L2*(2m1+m2-m2*cos(2θ1-2θ2))) I'll use RK4 integration for accuracy and a canvas with a fading trail. Let me make it visually stunning.
/tmp/ws/index.html (6852 bytes)Successfully wrote 6852 bytes to /tmp/ws/index.html
thinking
The file has been written. Let me verify it's present and has the right structure.
{"command":"ls -la /tmp/ws/index.html && wc -l /tmp/ws/index.html"}-rw-r--r--. 1 node node 6854 Aug 1 19:54 /tmp/ws/index.html 269 /tmp/ws/index.html
The file is ready at `/tmp/ws/index.html`. Here's what it includes: **Physics:** - Correct **Lagrangian-derived equations of motion** for a double pendulum (full nonlinear form, no small-angle approximations) - **4th-order Runge-Kutta integration** with sub-stepping for numerical stability - Proper coupling between both arms (the `alpha1` and `alpha2` terms include all cross-dependencies) **Visuals:** - **Colorful fading trail** of the second bob using HSL hue cycling — colors smoothly shift through the spectrum - Trail width and opacity fade from thick/bright at the tip to thin/faint at the tail - **Radial glow** around the bob tip - Gradient-shaded masses with a bright center dot on the bob - Subtle background ghosting for motion blur effect - Dark background with a soft purple shadow box **Controls:** - **Reset** button — randomizes initial angles and velocities each click - **Speed** slider — adjusts integration sub-steps per frame (1–8×) - **Trail** slider — adjusts trail length (50–2000 points) Open it in any browser — no network or dependencies needed.