Double pendulum · qwen3.8-2.4t-a95b
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 · 4 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
Write a single-file index.html: a double pendulum simulation using the correct equations of motion, RK4 integration, canvas drawing with a fading colorful trail, and probably controls. Self-contained.
/tmp/ws/index.html (11001 bytes)Successfully wrote 11001 bytes to /tmp/ws/index.html
thinking
Complete. Let me briefly summarize the main parts.
Created `/tmp/ws/index.html` — a fully self-contained double pendulum simulator, no external resources. **Physics (exact equations of motion):** - Standard Lagrangian-derived angular accelerations: - α₁ = [−g(2m₁+m₂)sinθ₁ − m₂g sin(θ₁−2θ₂) − 2sin(θ₁−θ₂)m₂(ω₂²L₂ + ω₁²L₁cos(θ₁−θ₂))] / [L₁(2m₁+m₂−m₂cos(2(θ₁−θ₂)))] - α₂ = [2sin(θ₁−θ₂)(ω₁²L₁(m₁+m₂) + g(m₁+m₂)cosθ₁ + ω₂²L₂m₂cos(θ₁−θ₂))] / [L₂(2m₁+m₂−m₂cos(2(θ₁−θ₂)))] - Integrated with **RK4** at 4 substeps per frame for accuracy/energy stability. **Visuals & features:** - Colorful tip trail cycling through HSL hues, fading out with quadratic alpha and growing width (600 segments). - Gradient-shaded bobs sized by mass, glowing tip, thin arms, subtle pivot. - Sliders for m₁, m₂, L₁, L₂, gravity, and sim speed. - **Drag either bob** with the mouse to reposition it live. - **Ghost button**: runs a second pendulum perturbed by just 1e-5 rad, drawn as a gray trail — a vivid demonstration of sensitive dependence on initial conditions (chaos). - Pause/Reset buttons, responsive full-window canvas with devicePixelRatio scaling.
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 trails and correct chaotic motion; sliders/controls present, animates continuously.
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.