Double pendulum · muse-wonder
Output generated Cost / run $0.5614 Runtime 104.5s
Prompt for this run
Build a planar double-pendulum simulation on a canvas with a colorful fading trail at the lower bob. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Model two point masses connected by massless rigid rods under gravity, without damping or external driving. Use the coupled equations of motion rather than independent sine-wave animations. - Use equal masses and rod lengths, gravity of 9.81 in consistent simulation units, initial angles of 120 and -10 degrees measured from downward vertical, and zero initial angular velocities. - Draw a fixed pivot, both rods and bobs, and a bounded fading trail of the lower bob. Keep both rod lengths constant and the pendulum visible. - Provide Pause/Resume and Reset. Reset restores the stated initial conditions and clears the trail. - Use a numerically stable integration scheme and time step so ordinary playback does not explode or freeze. Verify: Sample the pendulum at several moments to inspect coupled motion, connected rods, and the lower-bob trail. Pause and resume to check the motion control, then reset and confirm that the starting pose and cleared trail return.
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
METRICS
Transcript · 27 messages
Build a planar double-pendulum simulation on a canvas with a colorful fading trail at the lower bob. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Model two point masses connected by massless rigid rods under gravity, without damping or external driving. Use the coupled equations of motion rather than independent sine-wave animations. - Use equal masses and rod lengths, gravity of 9.81 in consistent simulation units, initial angles of 120 and -10 degrees measured from downward vertical, and zero initial angular velocities. - Draw a fixed pivot, both rods and bobs, and a bounded fading trail of the lower bob. Keep both rod lengths constant and the pendulum visible. - Provide Pause/Resume and Reset. Reset restores the stated initial conditions and clears the trail. - Use a numerically stable integration scheme and time step so ordinary playback does not explode or freeze. Verify: Sample the pendulum at several moments to inspect coupled motion, connected rods, and the lower-bob trail. Pause and resume to check the motion control, then reset and confirm that the starting pose and cleared trail return.
thinking
Designing a single-file HTML canvas implementation for a planar double pendulum with coupled equations, stable integration, and pause/reset controls.Adding RK4 integration, DPR-aware canvas scaling, and bounded fading trail rendering.
index.html (16183 bytes)Successfully wrote to index.html
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing.","error: Cannot read properties of undefined (reading 'length')"],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n⏸ Pause\n↺ Reset\nRunning\nSim time 0.00 s\nTrail 0 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n120.0°\nΘ₂ — LOWER ROD\n−10.0°\nΩ₁ — UPPER SPEED\n0.00 rad/s\nΩ₂ — LOWER SPEED\n0.00 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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Analyzing a JavaScript undefined error in draw() due to trail access before initialization during resize before resetSim.
{"path":"index.html","edits":[{"oldText":" var state, simTime, trail, running, hueSeed;","newText":" var state = { t1:INIT.t1, t2:INIT.t2,Successfully replaced 2 block(s) in index.html.
{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n⏸ Pause\n↺ Reset\nRunning\nSim time 0.11 s\nTrail 27 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n116.2°\nΘ₂ — LOWER ROD\n−11.7°\nΩ₁ — UPPER SPEED\n-1.14 rad/s\nΩ₂ — LOWER SPEED\n-0.48 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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{"action":"motion"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n⏸ Pause\n↺ Reset\nRunning\nSim time 4.28 s\nTrail 700 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n116.6°\nΘ₂ — LOWER ROD\n386.5°\nΩ₁ — UPPER SPEED\n-0.29 rad/s\nΩ₂ — LOWER SPEED\n0.36 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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Normalizing display angles to -180 to 180 for readability while keeping internal state unwrapped.
{"path":"index.html","edits":[{"oldText":" function fmtDeg(rad){ return (rad/DEG).toFixed(1)+'°'; }","newText":" function fmtDeg(rad){ varSuccessfully replaced 2 block(s) in index.html.
{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n⏸ Pause\n↺ Reset\nRunning\nSim time 0.11 s\nTrail 28 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n116.2°\nΘ₂ — LOWER ROD\n−11.7°\nΩ₁ — UPPER SPEED\n-1.14 rad/s\nΩ₂ — LOWER SPEED\n-0.48 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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{"action":"click","x":166,"y":151}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n▶ Resume\n↺ Reset\nPaused\nSim time 3.61 s\nTrail 700 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n-3.9°\nΘ₂ — LOWER ROD\n46.4°\nΩ₁ — UPPER SPEED\n5.45 rad/s\nΩ₂ — LOWER SPEED\n-1.09 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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{"action":"click","x":166,"y":151}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n⏸ Pause\n↺ Reset\nRunning\nSim time 3.68 s\nTrail 700 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n18.9°\nΘ₂ — LOWER ROD\n37.1°\nΩ₁ — UPPER SPEED\n6.55 rad/s\nΩ₂ — LOWER SPEED\n-3.76 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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{"action":"click","x":166,"y":151}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n▶ Resume\n↺ Reset\nPaused\nSim time 8.13 s\nTrail 700 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n9.8°\nΘ₂ — LOWER ROD\n14.8°\nΩ₁ — UPPER SPEED\n7.34 rad/s\nΩ₂ — LOWER SPEED\n-5.39 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
{"action":"click","x":287,"y":151}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum Chaos\n\nTwo equal point masses on massless rigid rods, solved with the true coupled equations of motion under gravity — no sine-wave shortcuts. Small changes grow into wildly different paths.\n\n● RK4 integrator · g = 9.81 m/s² · no damping\n▶ Resume\n↺ Reset\nPaused\nSim time 0.00 s\nTrail 1 pts\n🌈 trail = path of lower bob (fades & is capped)\nΘ₁ — UPPER ROD\n120.0°\nΘ₂ — LOWER ROD\n−10.0°\nΩ₁ — UPPER SPEED\n0.00 rad/s\nΩ₂ — LOWER SPEED\n0.00 rad/s\nInitial conditions (Reset): θ₁ = 120°, θ₂ = −10° from the downward vertical, ω₁ = ω₂ = 0. Equal masses m₁ = m₂ = 1 and equal rods L₁ = L₂ = 1 m.\nNumerics: classic 4th-order Runge–Kutta at a fixed dt = 1/480 s with a frame-time accumulator (clamped to avoid spiral-of-death). Energy stays bounded, rods stay exactly L long by construction.\nAngles are measured from the downward vertical. The trail stores at most 700 points and older points fade out — it is redrawn from positions, never allowed to grow without bound.","images":"attached"}
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{"command":"ls -lh index.html && grep -nE \"https?://|src=|cdn\" index.html || echo \"no external refs\""}-rw-r--r-- 1 node node 17K Oct 15 04:05 index.html no external refs
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Built `index.html` — a self-contained planar double-pendulum simulation (no external assets/CDNs): - **Physics:** True coupled double-pendulum equations of motion (Lagrangian form), equal masses `m₁=m₂=1`, equal rods `L₁=L₂=1 m`, `g=9.81`, no damping/driving. Integrated with fixed-step RK4 (`dt=1/480 s`) + clamped accumulator for stability. - **Initial conditions:** θ₁=120°, θ₂=−10° from downward vertical, ω₁=ω₂=0. - **Rendering:** Canvas with fixed pivot, both constant-length rods/bobs, live θ/ω/time readouts, and a colorful rainbow trail of the lower bob capped at 700 points with older points fading out. - **Controls:** Pause/Resume (also Space) and Reset. **Verified in browser:** - Initial startup error (trail accessed before initialization) was found and fixed; console now clean. - Sampled motion at several moments (~0.1s, 2.5s, 3.1s, 3.7s, 4.3s): coupled chaotic motion including lower-rod flips, rods stay connected, trail builds and saturates at exactly 700 pts. - Pause froze the state (button switched to “Resume”, status “Paused”); Resume restarted motion and sim time advanced. - Reset while paused restored exactly θ₁=120.0°, θ₂=−10.0°, ω=0.00, time 0.00 s, and cleared the trail to 1 pt, with the starting pose redrawn. **Unverified:** Long-run (minutes-scale) energy drift and behavior on small/mobile viewports were not exhaustively tested, though the fixed small RK4 step and bounded trail are designed to keep both stable.