Double pendulum · minimax-m2.7
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 double pendulum simulation with: 1. Correct equations of motion for a double pendulum 2. Canvas-based rendering 3. Arms drawing 4. Colorful fading trail of the tip Let me create a single HTML file with everything inline. I'll need to implement: - The physics equations for a double pendulum - Canvas drawing - Trail effect with fading The double pendulum equations are well-known. For a double pendulum with masses m1, m2 and lengths L1, L2: The equations of motion are derived from Lagrangian mechanics: δ²θ₁/δt² = -g(2m₁+m₂)sin(θ₁) - m₂g sin(θ₁-2θ₂) - 2sin(θ₁-θ₂)m₂(ω₂²L₂+ω₁²L₁cos(θ₁-θ₂)) / (m₁+m₂)L₁ δ²θ₂/δt² = 2sin(θ₁-θ₂)(ω₁²L₁(m₁+m₂) + g(m₁+m₂)cos(θ₁) + ω₂²L₂m₂cos(θ₁-θ₂)) / (m₁+m₂)L₂ Or using the more standard form with the denominator D: D = 2(m₁+m₂) - m₂cos(2θ₁-2θ₂) For θ₁: num1 = -g(2m₁+m₂)sin(θ₁) - m₂(2m₁+m₂)gsin(θ₁-2θ₂) - 2sin(θ₁-θ₂)m₂(ω₂²L₂ + ω₁²L₁cos(θ₁-θ₂)) Dθ₁/Dt² = num1 / (m₁+m₂)L₁D For θ₂: num2 = 2sin(θ₁-θ₂)(ω₁²L₁(m₁+m₂) + g(m₁+m₂)cos(θ₁) + ω₂²L₂m₂cos(θ₁-θ₂)) Dθ₂/Dt² = num2 / (m₁+m₂)L₂D Now I'll build out the complete HTML file with the physics simulation and rendering.
/workspace/index.html (12854 bytes)Successfully wrote 12854 bytes to /workspace/index.html
thinking
I've created a complete double pendulum simulation. Let me verify the file exists and summarize what I built.
{"command":"ls -la /workspace/index.html"}-rw-r--r-- 1 node node 12854 Jul 8 00:45 /workspace/index.html
thinking
The file was created successfully. Let me provide a summary of what was built.
Done! I've created a **chaotic double pendulum simulation** in `/workspace/index.html`. ### Features: **Physics:** - Accurate equations of motion using Lagrangian mechanics - RK4 integration for numerical stability - Configurable masses, lengths, and damping - True chaotic behavior emerges from sensitivity to initial conditions **Visuals:** - Colorful fading trail that cycles through hues based on position in the trail history - Gradient-colored arms (purple → pink) - Glowing mass nodes with size proportional to mass - Motion blur effect via semi-transparent clearing **Interactive Controls:** - **Sliders:** Adjust mass 1/2, length 1/2, damping, trail length - **Reset button:** Randomize initial conditions - **Clear Trail button:** Erase the trail without changing state - **Click anywhere:** Apply impulse to the pendulum (direction based on click position) - **Window resize:** Responsive canvas ### The Double Pendulum: A double pendulum is a classic example of chaotic dynamics — it exhibits sensitive dependence on initial conditions, meaning tiny differences in starting angles lead to vastly different trajectories. Despite following deterministic equations, its motion is fundamentally unpredictable over long times. Open `index.html` in a browser to see it in action. Try setting different masses/lengths and clicking to perturb it and watch the chaos unfold!
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, responds to clicks/drags/keys with impulses, though idle motion is absent until interaction.
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.