Double pendulum · qwen3.5-397b-a17b
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.
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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 (Lagrangian mechanics) 2. Canvas rendering 3. Arms drawn 4. Colorful fading trail of the tip I need to implement the physics equations for a double pendulum. The equations of motion can be derived from the Lagrangian. Let me create a self-contained HTML file with all the CSS and JavaScript inline. The double pendulum equations are quite complex. I'll use the standard form derived from the Lagrangian mechanics: For a double pendulum with: - m1, m2: masses - l1, l2: lengths - θ1, θ2: angles from vertical - g: gravity The angular accelerations are: θ1'' = [ -g(2m1+m2)sin(θ1) - m2g sin(θ1-2θ2) - 2sin(θ1-θ2)m2(θ2'²l2 + θ1'²l1cos(θ1-θ2)) ] / [ l1(2m1+m2-m2cos(2θ1-2θ2)) ] θ2'' = [ 2sin(θ1-θ2)(θ1'²l1(m1+m2) + g(m1+m2)cos(θ1) + θ2'²l2m2cos(θ1-θ2)) ] / [ l2(2m1+m2-m2cos(2θ1-2θ2)) ] I'll implement this with Runge-Kutta integration for accuracy, draw the pendulum arms, and create a colorful fading trail.
/tmp/ws/index.html (9599 bytes)Successfully wrote 9599 bytes to /tmp/ws/index.html
thinking
I've created a complete single-page web app that simulates a chaotic double pendulum. The file includes: 1. **Correct equations of motion**: Using Lagrangian mechanics to derive the angular accelerations for both pendulum arms 2. **RK4 integration**: Runge-Kutta 4th order numerical integration for accurate physics simulation 3. **Canvas rendering**: Drawing the pendulum arms, joints, and origin point 4. **Colorful fading trail**: The tip leaves a rainbow-colored trail that fades and cycles through hues 5. **Interactive controls**: Reset, Randomize, and Toggle Trail buttons 6. **All inline**: CSS in `<style>` tag, JS in `<script>` tag, no external resources The simulation demonstrates the famous chaotic behavior of the double pendulum - tiny changes in initial conditions lead to dramatically different trajectories.
Created `index.html` with a complete double pendulum simulation featuring: - **Accurate physics**: Lagrangian equations of motion with RK4 numerical integration - **Visual elements**: Two arms with colored joints, origin pivot point - **Colorful fading trail**: Rainbow gradient trail that follows the tip position - **Interactive controls**: Reset, Randomize, and Toggle Trail buttons - **Self-contained**: All CSS and JavaScript inline, no external dependencies Open the file in a browser to see the chaotic motion - the system is highly sensitive to initial conditions, demonstrating classic chaos theory behavior.
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 smoothly with colorful fading tip trail; simple UI, buttons present but no clear pointer/keyboard interaction difference.
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.