Double pendulum · laguna-xs-2.1

Output saved · Timed out Cost / run $0.0111 Runtime 900.1s

The 15-minute session limit cut this run off. The output is the HTML saved at that point.

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.

⛨ sandboxed Open in new tab ↗

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

modellaguna-xs-2.1

vendorpoolside

harnesspi 0.87.1 · browser iteration

generated2026-10-07

METRICS

runtime900.1s

tokens in299k

tokens out13k

cached277k

cost / run$0.0111

Transcript · 51 messages

system

user

assistant

thinking

Let me build a double pendulum simulation. I need to:

1. Create a single HTML file with inline CSS and JavaScript
2. Implement the physics of a double pendulum using the coupled equations of motion
3. Add a canvas with:
   - Fixed pivot
   - Two rods and bobs
   - Fading trail for the lower bob
4. Add Pause/Resume and Reset buttons
5. Use equal masses and rod lengths, gravity of 9.81
6. Initial angles: 120 and -10 degrees from downward vertical, zero initial angular velocities
7. Use a numerically stable integration scheme (I'll use RK4 or Verlet integration)

Let me write the complete index.html file.

The double pendulum equations of motion are complex. For a double pendulum with:
- m1, m2: masses
- l1, l2: rod lengths
- θ1, θ2: angles from vertical
- ω1, ω2: angular velocities

The equations are:

α1 = (-g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2*sin(θ1-θ2)*m2*(ω2²*l2 + ω1²*l1*cos(θ1-θ2))) / (l1*(2m1+m2-m2*cos(2θ1-2θ2)))

α2 = (2*sin(θ1-θ2)*(ω1²*l1*(m1+m2) + g*(m1+m2)*cos(θ1) + ω2²*l2*m2*cos(θ1-θ2))) / (l2*(2m1+m2-m2*cos(2θ1-2θ2)))

I'll use RK4 integration for numerical stability.

Let me create the file now.

→ write /app/pipeline/node_modules/@earendil-works/pi-coding-agent/docs/../index.html (7033 bytes)

toolResult

EACCES: permission denied, open '/app/pipeline/node_modules/@earendil-works/pi-coding-agent/index.html'

assistant

thinking

I need to write to the current working directory, not that nested path. Let me check the current working directory and write there.

→ bash {"command":"pwd && ls -la"}

toolResult

/tmp/job-6aQXyk total 12 drwx------ 3 node node 4096 Oct 7 02:23 . drwxrwxrwt 6 root root 4096 Oct 7 02:23 .. drwxr-xr-x 3 node node 4096 Oct 7 02:23 .home

assistant

thinking

The current working directory is /tmp/job-6aQXyk. Let me write the index.html file there.

→ write /tmp/job-6aQXyk/index.html (7066 bytes)

toolResult

Successfully wrote to /tmp/job-6aQXyk/index.html

assistant

thinking

The file has been written. Now let me run the browser to test the simulation.

Now let me run the browser to test the simulation:

→ browser {"action":"reload"}

toolResult

{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Double Pendulum\nPause\nReset","images":"model does not support images"}

assistant

thinking

Good, the page loaded. Let me inspect the canvas and interact with the controls to verify the simulation is working correctly.

→ browser {"action":"inspect"}

toolResult

assistant

thinking

Let me take a screenshot to see the visual output.

→ browser {"action":"screenshot"}

toolResult

assistant

thinking

The screenshot didn't work as expected. Let me try clicking the buttons to verify the controls work.

→ browser {"action":"click","x":130,"y":50}

toolResult

assistant

thinking

Let me check the Reset button and also check if there are any issues. Let me also click the Pause button. The coordinates might be off. Let me try different coordinates based on the expected layout.

Actually, let me check the console to see if there are any errors.

→ browser {"text":"document.querySelector('#pauseBtn').textContent"}

toolResult

Validation failed for tool "browser": - action: must have required properties action Received arguments: { "text": "document.querySelector('#pauseBtn').textContent" }

assistant

thinking

The browser tool doesn't support text evaluation. Let me try clicking the buttons at reasonable coordinates. The pause button should be around x=130 (first button), and the reset button around x=250.

Let me try clicking the Pause button first:

→ browser {"action":"click","x":130,"y":30}

toolResult

assistant

thinking

Let me check if the button click was successful by looking at the DOM text. The DOM shows "Pause\nReset" which suggests the button text hasn't changed, meaning perhaps the click didn't register or the page didn't fully load.

Let me try typing a command in the browser's console to check if the simulation is running and if buttons work:

→ browser {"action":"type","text":"document.querySelector('#pauseBtn').click()"}

toolResult

assistant

thinking

Let me try clicking on a different area - perhaps the Reset button:

→ browser {"action":"click","x":250,"y":30}

toolResult

assistant

thinking

The simulation is loading but the browser tool doesn't seem to capture the visual state well. Let me verify the file was written correctly and check for any JavaScript errors. Let me also check if the simulation is actually running by waiting a moment and checking again.

Let me try a different approach - let me scroll or wait a moment:

→ bash {"command":"sleep 2 && cat /tmp/job-6aQXyk/index.html | head -50"}

toolResult

assistant

thinking

The file looks correct. Let me verify the full file is there and then check if there might be an issue with the physics. Let me look at the key physics function to ensure it's correct.

Actually, I notice a potential issue - the canvas height is 600 and I'm using CY = canvas.height / 2 = 300, which places the pivot in the middle of the canvas. That should be fine.

Let me also check that the initial angles are correct. The angles are measured from the downward vertical, so:
- theta1 = 120° means the first rod should be swinging to the left (counterclockwise from vertical)
- theta2 = -10° means the second rod is slightly to the right of vertical (clockwise from vertical)

Let me verify the physics equations are correct. The double pendulum equations are complex. Let me re-check them.

Actually, I think there might be an issue with my RK4 implementation. Let me fix it to be more numerically stable and also verify the equations.

The standard double pendulum equations are:

For the accelerations:
α1 = (-g(2m1+m2)sin(θ1) - m2*g*sin(θ1-2θ2) - 2*sin(θ1-θ2)*m2*(ω2²*l2 + ω1²*l1*cos(θ1-θ2))) / (l1*(2m1+m2-m2*cos(2θ1-2θ2)))

α2 = (2*sin(θ1-θ2)*(ω1²*l1*(m1+m2) + g*(m1+m2)*cos(θ1) + ω2²*l2*m2*cos(θ1-θ2))) / (l2*(2m1+m2-m2*cos(2θ1-2θ2)))

My implementation looks correct. Let me also check the RK4 step - I think there might be an issue with how I'm computing k3 and k4.

Let me rewrite the RK4 integration to be more accurate:

In RK4:
k1 = f(t, y)
k2 = f(t + dt/2, y + dt*k1/2)
k3 = f(t + dt/2, y + dt*k2/2)
k4 = f(t + dt, y + dt*k3)

y_new = y + dt/6 * (k1 + 2*k2 + 2*k3 + k4)

For the double pendulum, the state is [θ1, ω1, θ2, ω2], and the derivative function is:
d(θ1)/dt = ω1
d(ω1)/dt = α1(θ1, ω1, θ2, ω2)
d(θ2)/dt = ω2
d(ω2)/dt = α2(θ1, ω1, θ2, ω2)

So for the RK4, I need to compute the derivatives at each stage.

Let me rewrite this more carefully:

Let me check if there's an issue with the simulation. Let me read the full file and then check the physics:

→ read {"path":"/tmp/job-6aQXyk/index.html"}

toolResult

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Double Pendulum Simulation</title> <style> * { margin: 0; padding: 0; box-sizing: border-box; } body { display: flex; flex-direction: column; align-items: center; justify-content: flex-start; background: #111; min-height: 100vh; font-family: Arial, sans-serif; } .controls { margin-top: 15px; display: flex; gap: 10px; } button { padding: 10px 20px; font-size: 16px; cursor: pointer; background: #4a90a4; color: white; border: none; border-radius: 5px; transition: background 0.2s; } button:hover { background: #5aa8b8; } button:active { background: #357a8f; } canvas { background: #222; border: 2px solid #555; margin-top: 10px; } </style> </head> <body> <h1 style="color:#fff; margin-top:15px;">Double Pendulum</h1> <div class="controls"> <button id="pauseBtn">Pause</button> <button id="resetBtn">Reset</button> </div> <canvas id="canvas" width="800" height="600"></canvas> <script> (() => { const canvas = document.getElementById('canvas'); const ctx = canvas.getContext('2d'); const pauseBtn = document.getElementById('pauseBtn'); const resetBtn = document.getElementById('resetBtn'); // Physical constants const G = 9.81; const L = 100; // rod length (pixels) const M = 1; // mass (equal) const DT = 0.016; // time step ~60 FPS // Canvas center const CX = canvas.width / 2; const CY = canvas.height / 2; // pivot Y offset from top // State: [theta1, omega1, theta2, omega2] // Initial angles: 120° and -10° from downward vertical const initialAngles = { theta1: 120 * Math.PI / 180, theta2: -10 * Math.PI / 180 }; let state = [initialAngles.theta1, 0, initialAngles.theta2, 0]; let trail = []; let running = true; let lastTimestamp = 0; // Trail parameters const maxTrailLength = 200; const trailAlpha = 0.003; // fading factor per point function computeAccelerations(theta1, omega1, theta2, omega2) { const delta = theta1 - theta2; const cosDelta = Math.cos(delta); const sinDelta = Math.sin(delta); const denom = 2 * M + M - M * Math.cos(2 * delta); // α1 const num1 = -G * (2 * M + M) * Math.sin(theta1) - M * G * Math.sin(theta1 - 2 * theta2) - 2 * sinDelta * M * (omega2 * omega2 * L + omega1 * omega1 * L * cosDelta); const alpha1 = num1 / (L * denom); // α2 const num2 = 2 * sinDelta * (omega1 * omega1 * L * (M + M) + G * (M + M) * Math.cos(theta1) + omega2 * omega2 * L * M * cosDelta); const alpha2 = num2 / (L * denom); return [alpha1, alpha2]; } // RK4 integration function rk4Step(s, dt) { const [theta1, omega1, theta2, omega2] = s; // k1 const [a1_k1, a2_k1] = computeAccelerations(theta1, omega1, theta2, omega2); // k2 const [a1_k2, a2_k2] = computeAccelerations( theta1 + 0.5 * dt * omega1, omega1 + 0.5 * dt * a1_k1, theta2 + 0.5 * dt * omega2, omega2 + 0.5 * dt * a2_k1 ); // k3 const [a1_k3, a2_k3] = computeAccelerations( theta1 + 0.5 * dt * (omega1 + 0.5 * dt * a1_k1), omega1 + 0.5 * dt * a1_k2, theta2 + 0.5 * dt * (omega2 + 0.5 * dt * a2_k1), omega2 + 0.5 * dt * a2_k2 ); // k4 const [a1_k4, a2_k4] = computeAccelerations( theta1 + dt * (omega1 + 0.5 * dt * a1_k3), omega1 + dt * a1_k3, theta2 + dt * (omega2 + 0.5 * dt * a2_k3), omega2 + dt * a2_k3 ); const newTheta1 = theta1 + dt * (omega1 + dt * (a1_k1 + 2*a1_k2 + 2*a1_k3 + a1_k4) / 6); const newOmega1 = omega1 + dt * (a1_k1 + 2*a1_k2 + 2*a1_k3 + a1_k4) / 6; const newTheta2 = theta2 + dt * (omega2 + dt * (a2_k1 + 2*a2_k2 + 2*a2_k3 + a2_k4) / 6); const newOmega2 = omega2 + dt * (a2_k1 + 2*a2_k2 + 2*a2_k3 + a2_k4) / 6; return [newTheta1, newOmega1, newTheta2, newOmega2]; } function update(dt) { state = rk4Step(state, dt); // Position of lower bob const x1 = CX + L * Math.sin(state[0]); const y1 = CY + L * Math.cos(state[0]); const x2 = x1 + L * Math.sin(state[1]); const y2 = y1 + L * Math.cos(state[1]); // Add to trail trail.push({x: x2, y: y2}); if (trail.length > maxTrailLength) { trail.shift(); } } function draw() { ctx.clearRect(0, 0, canvas.width, canvas.height); // Draw trail with fading effect ctx.fillStyle = 'rgba(255, 200, 50, 0.6)'; for (let i = 0; i < trail.length - 1; i++) { const alpha = trailAlpha * (i + 1); const p1 = trail[i]; const p2 = trail[i + 1]; ctx.globalAlpha = alpha; ctx.beginPath(); ctx.moveTo(p1.x, p1.y); ctx.lineTo(p2.x, p2.y); ctx.lineWidth = 3; ctx.lineCap = 'round'; ctx.stroke(); } ctx.globalAlpha = 1; // Positions const x1 = CX + L * Math.sin(state[0]); const y1 = CY + L * Math.cos(state[0]); const x2 = x1 + L * Math.sin(state[1]); const y2 = y1 + L * Math.cos(state[1]); // Draw pivot ctx.fillStyle = '#fff'; ctx.beginPath(); ctx.arc(CX, CY, 8, 0, 2 * Math.PI); ctx.fill(); // Draw rod 1 ctx.strokeStyle = '#88c0d0'; ctx.lineWidth = 4; ctx.beginPath(); ctx.moveTo(CX, CY); ctx.lineTo(x1, y1); ctx.stroke(); // Draw rod 2 ctx.beginPath(); ctx.moveTo(x1, y1); ctx.lineTo(x2, y2); ctx.stroke(); // Draw bobs const bobRadius = 18; // Bob 1 ctx.fillStyle = '#5e81ac'; ctx.beginPath(); ctx.arc(x1, y1, bobRadius, 0, 2 * Math.PI); ctx.fill(); ctx.strokeStyle = '#81a1c1'; ctx.lineWidth = 2; ctx.stroke(); // Bob 2 ctx.fillStyle = '#a3be8c'; ctx.beginPath(); ctx.arc(x2, y2, bobRadius, 0, 2 * Math.PI); ctx.fill(); ctx.strokeStyle = '#88c0d0'; ctx.lineWidth = 2; ctx.stroke(); } function loop(timestamp) { if (!running) return; if (lastTimestamp === 0) lastTimestamp = timestamp; const delta = (timestamp - lastTimestamp) / 1000; lastTimestamp = timestamp; update(delta * (DT / 0.016)); // normalize to sim time step draw(); requestAnimationFrame(loop); } function reset() { state = [initialAngles.theta1, 0, initialAngles.theta2, 0]; trail = []; pauseBtn.textContent = 'Pause'; running = true; lastTimestamp = 0; requestAnimationFrame(loop); } function togglePause() { running = !running; pauseBtn.textContent = running ? 'Pause' : 'Resume'; if (running) { lastTimestamp = 0; requestAnimationFrame(loop); } } pauseBtn.addEventListener('click', togglePause); resetBtn.addEventListener('click', reset); // Initial draw draw(); requestAnimationFrame(loop); })(); </script> </body> </html>

assistant

thinking

I see there's an issue with my RK4 implementation. The way I'm computing k3 and k4 is incorrect. Let me rewrite the integration more carefully.

The RK4 method for a system of ODEs:
- State vector y = [θ1, ω1, θ2, ω2]
- Derivatives: dy/dt = [ω1, α1, ω2, α2]

For RK4:
k1 = f(y)
k2 = f(y + dt/2 * k1)
k3 = f(y + dt/2 * k2)
k4 = f(y + dt * k3)
y_new = y + dt/6 * (k1 + 2*k2 + 2*k3 + k4)

I need to define a proper derivative function and use it correctly.

Also, I notice the loop function is using delta time in a strange way. Let me simplify and fix this.

Let me rewrite the file with a corrected implementation:

I see there are issues with the physics integration. Let me fix the RK4 implementation and the time stepping:

→ write /tmp/job-6aQXyk/index.html (7431 bytes)

toolResult

Successfully wrote to /tmp/job-6aQXyk/index.html

assistant

thinking

Now let me test the simulation in the browser again.

→ browser {"action":"reload"}

toolResult

assistant

thinking

Let me try to take a screenshot to see the initial state of the canvas:

→ browser {"action":"screenshot"}

toolResult

assistant

thinking

The browser tool doesn't give me visual output. Let me try a different approach - let me scroll to see if the simulation is running:

→ browser {"action":"scroll","delta":100}

toolResult

assistant

thinking

Let me check if the simulation is working by looking at the DOM. The elements are there. Let me try clicking the reset button to test it:

→ browser {"action":"click","x":250,"y":30}

toolResult

assistant

thinking

The DOM shows "Pause\nReset" which means the buttons are there. Let me try clicking the Pause button (first button) and see if the text changes:

→ browser {"action":"click","x":130,"y":30}

toolResult

assistant

thinking

The browser tool seems to have issues capturing the state. Let me try a different approach - let me type a JavaScript command to interact with the page:

→ bash

{"command":"cd /tmp/job-6aQXyk && html-preview index.html 2>/dev/null || echo \"No html-preview available, checking syntax\""}

toolResult

No html-preview available, checking syntax

assistant

thinking

Let me verify the file is syntactically correct by checking with node:

→ bash

{"command":"cd /tmp/job-6aQXyk && node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('index.html', 'utf8');\n\n// Check for

toolResult

DOCTYPE: true Canvas: true Script: true Buttons: true

assistant

thinking

The HTML file structure looks good. Let me also verify the JavaScript logic by running it through a quick syntax check:

→ bash

{"command":"cd /tmp/job-6aQXyk && node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('index.html', 'utf8');\n\n// Extract t

toolResult

JavaScript syntax: VALID

assistant

thinking

The JavaScript syntax is valid. Now let me verify the physics by running a quick simulation test:

→ bash

{"command":"cd /tmp/job-6aQXyk && node -e \"\n// Extract and run the physics simulation\nconst fs = require('fs');\nconst html = fs.readFile

toolResult

Error: requestAnimationFrame is not defined

assistant

thinking

The script needs requestAnimationFrame. Let me add that to the global scope and try again:

→ bash

{"command":"cd /tmp/job-6aQXyk && node -e \"\n// Extract and run the physics simulation\nconst fs = require('fs');\nconst html = fs.readFile

toolResult

Error: mockCtx is not a function TypeError: mockCtx is not a function at Object.getContext ([eval]:19:31) at eval (eval at <anonymous> ([eval]:68:9), <anonymous>:4:22) at eval (eval at <anonymous> ([eval]:68:9), <anonymous>:228:3) at [eval]:68:9 at runScriptInThisContext (node:internal/vm:219:10) at node:internal/process/execution:451:12 at [eval]-wrapper:6:24 at runScriptInContext (node:internal/process/execution:449:60) at evalFunction (node:internal/process/execution:283:30) at evalTypeScript (node:internal/process/execution:295:3)

assistant

thinking

There's a syntax error in my mock. Let me fix it:

→ bash

{"command":"cd /tmp/job-6aQXyk && node -e \"\n// Extract and run the physics simulation\nconst fs = require('fs');\nconst html = fs.readFile