Double pendulum · qwen3.5-27b
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 double pendulum with: 1. Correct equations of motion for a double pendulum 2. Canvas-based visualization 3. Drawing the two arms 4. A colorful fading trail following the tip Let me write this as a complete index.html file with embedded CSS and JavaScript. For a double pendulum, I need to use Lagrangian mechanics. The equations of motion are: Given: - m1, m2 = masses of first and second bob - l1, l2 = lengths of first and second arm - θ1, θ2 = angles from vertical - θ̇1, θ̇2 = angular velocities - g = gravity constant The equations of motion (derived from Lagrangian): θ̈₁ = (-g(2m₁ + m₂)sin(θ₁) - m₂g sin(θ₁ - 2θ₂) - 2sin(θ₁ - θ₂)m₂(l₂θ̇₂² + l₁θ̇₁²cos(θ₁ - θ₂))) / (l₁(2m₁ + m₂ - m₂cos(2θ₁ - 2θ₂))) θ̈₂ = (2sin(θ₁ - θ₂)(l₁θ̇₁²(m₁ + m₂) + g(m₁ + m₂)cos(θ₁) + l₂θ̇₂²m₂cos(θ₁ - θ₂))) / (l₂(2m₁ + m₂ - m₂cos(2θ₁ - 2θ₂))) Let me implement this properly in JavaScript.
/tmp/ws/index.html (9750 bytes)Successfully wrote 9750 bytes to /tmp/ws/index.html
thinking
I've created a complete single-page web app that simulates a chaotic double pendulum. Let me verify the file was created correctly.
{"command":"ls -la /tmp/ws/index.html"}-rw-r--r--. 1 node node 9752 Aug 1 19:52 /tmp/ws/index.html
thinking
The file has been created successfully. Let me provide a summary of what I've built.
Done! Created `index.html` with a complete chaotic double pendulum simulation featuring: **Physics:** - Correct Lagrangian equations of motion for a double pendulum - Runge-Kutta 4th order (RK4) numerical integration for accuracy - Realistic parameters (masses, lengths, gravity) **Visuals:** - Two colored arms with gradient spheres at each joint - Rainbow fading trail following the tip bob - Glow effect around the moving tip - Dark themed UI with modern styling **Controls:** - **Reset** button - randomizes initial conditions (each reset produces different chaotic behavior) - **Toggle Trail** button - show/hide the colorful path Open the file in a browser to see the mesmerizing chaotic motion. Each run is unique due to sensitivity to initial conditions—the hallmark of chaos theory!
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 animates continuously with colorful fading trail; matches prompt well, no distinct input-specific interactivity observed.
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.