Double pendulum · muse-glimmer-30b
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 · 8 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
Simulate a chaotic double pendulum on a canvas using correct equations of motion, drawing arms and colorful fading trail of tip. Build single-page web app write it ALL into one self-contained file named index.html in current directory: CSS in <style>, JS in <script>, inline — do not create separate .css/.js files. Use NO external resources, CDNs or network requests. We need write index.html. Use canvas. Double pendulum equations. Standard equations: Let l1,l2, m1,m2, g. θ1, θ2 angles from vertical. ω1, ω2 angular velocities. Equations: den1 = l1*(2*m1 + m2 - m2*cos(2θ1 - 2θ2)) num1 = -g*(2*m1+m2)*sinθ1 - m2*g*sin(θ1-2θ2) - 2*sin(θ1-θ2)*m2*(ω2^2*l2 + ω1^2*l1*cos(θ1-θ2)) α1 = num1 / den1 den2 = l2*(2*m1 + m2 - m2*cos(2θ1-2θ2)) num2 = 2*sin(θ1-θ2)*( ω1^2*l1*(m1+m2) + g*(m1+m2)*cosθ1 + ω2^2*l2*m2*cos(θ1-θ2) ) α2 = num2 / den2 That's standard. Alternatively use Lagrangian. We'll implement simulation with RK4 or simple Euler with small dt. Better use semi-implicit Euler or RK4 for stability. We'll draw arms and trail with fading. Colorful fading trail: we can store points array, draw with gradient opacity. Make controls? Might be nice to have reset button and sliders for masses/lengths? Could keep simple. Requirement: single file. No external resources. Implement canvas full window. Use requestAnimationFrame. Draw arms: lines from origin (center top) to bob1 to bob2. Trail: keep array of last N points (~500). Draw lines with color cycling hue based on time or position. Colorful fading: use HSL hue = (time*... ) % 360. Make background dark. Implement with correct equations. Let's create index.html. We need ensure no external resources. Use pure JS. Potential improvements: use devicePixelRatio. We'll write file. Let's check current directory.
{"command":"pwd && ls -la"}/tmp/ws total 0 drwxr-sr-x. 2 node node 6 Aug 13 01:25 . drwxrwsrwx. 3 root node 16 Aug 13 01:25 ..
thinking
Write index.html.
/tmp/ws/index.html (6152 bytes)Successfully wrote 6152 bytes to /tmp/ws/index.html
thinking
We wrote file. Should confirm exists.
{"command":"ls -l /tmp/ws/index.html && head -c 200 /tmp/ws/index.html"}-rw-r--r--. 1 node node 6154 Aug 13 01:25 /tmp/ws/index.html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>Chaotic Double Pendulum</title> <meta name="viewport" content="width=device-width,initial-scale=1"> <style> html,body{margin:0;hei
thinking
Done. Provide summary.
Created a self-contained double pendulum simulation at **/tmp/ws/index.html**. It uses the correct Lagrangian equations of motion with RK4 integration, draws the two arms from a fixed pivot, and renders a colorful fading trail for the second bob. The UI lets you adjust lengths/masses, reset, toggle trail, and click-drag to give impulses — all in one HTML file with inline CSS/JS and no external resources. Open `index.html` in a browser to see the chaotic motion.
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 simulates chaotic motion with colorful fading tip trail, though clicking seems to reset/freeze it oddly.
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.