Double pendulum · qwen3.8-max-0902

Let me build the index.html with RK4 integration.

Trail: store points array bounded, fading colors.

Canvas fixed size, draw with dark background. Add controls.

Let me write it.

The trail recording: I push only every 4 steps which is ~150Hz -> 900 points = 6 seconds of trail. Fine.

But note: hue assignment changes with steps%4 condition — fine.

Let me open in browser.

Working. Energy is conserved (E = E0 = 0.1490). The trail is barely visible at t=0.26s (only a tiny orange streak). Let me sample a few moments later to check the trail. Wait a bit, then take a screenshot. Use browser motion or screenshot after some time. The browser tool's "motion" captures frames over time. Let me take a screenshot after a few seconds.

Also, the HUD text is all on one line (I used \n in textContent, but since there's no white-space: pre, it doesn't render as line breaks). Fix: set white-space: pre-line on #hud.

Let me sample the state at several time points via the exposed API and verify the coupled motion and energy conservation over longer times. Use evaluate? The browser tool doesn't have evaluate... Actions: reload, inspect, screenshot, motion, click, drag, key, type, scroll. No JS eval. Hmm. "inspect" might return DOM/console. Can't run arbitrary JS. But I can verify with screenshots over time and clicks on Pause/Reset.

Alternatively, verify physics with node? I can run a simple node script that reproduces the RK4 to check energy conservation and rod length constancy. That's independent of the page but verifies the equations. Good idea.

First fix the HUD's white-space. Then take motion frames.

Next, I'll verify the physics independently with node (energy conservation over a long run, rod constraints are structurally implicit). After that, reload the browser and capture motion frames for the trail.

Physics simulation is extremely stable: over 120 seconds of simulation, energy drift is about 8e-7 (relative ~5e-6). Chaotic coupled motion confirmed (angles vary wildly, θ2 rotates multiple times).

Next, reload the browser and capture motion frames to check the trajectory. Use the "motion" action to get frames over time.

The HUD is now displayed in multiple lines. The trail (trajectory) still isn't visible at t=0.10s. Let's capture motion frames over several seconds to check the trail.

The trajectory is colorful and fading, the rods are connected, and the motion is coupled/chaotic. Energy is conserved. Next, test pause/resume and reset.

Click pause, take a screenshot, then take another screenshot about 1 second later to confirm that the state hasn't changed. After that, resume, then reset and confirm that the pose has returned to θ1=120, θ2=-10 and that the trajectory has been cleared.

Paused at t=12.32s. Verify that it's really frozen: take another screenshot about 1 second later and confirm that t hasn't changed. Use inspect (which returns the DOM after some delay), or take a screenshot. The screenshot action is nearly immediate. Better approach: take a screenshot now, then take another one after that. The time between tool calls is real time. Let me try calling screenshot twice.

The state is identical (t=12.32, same angle) — confirmed to be frozen. Next, click Resume, then click Reset, and verify the initial pose and that the trail has been cleared.

Resumed (t is progressing from 12.32 → 12.33+). Next, click Reset and verify the initial pose (θ1=120°, θ2=-10°) and that the trail has been cleared.

Reset works correctly: t≈0, θ₁=120.0°, θ₂=-10.0°, ω≈0, trail cleared (no trail in the image). Everything verified:

- Coupled equations of motion (standard double pendulum ODEs), RK4 with fixed DT=1/600, energy drift ~8e-7 over 120 seconds.
- Initial conditions exactly as specified.
- Fixed pivot, rods, bobs, bounded fading colorful trail (max 900 points).
- Rod length is constant by construction (angles parameterize positions).
- Verified pause/resume (state frozen and then resumes).
- Verified reset (pose + trail cleared).
- No console errors (only sandbox iframe warnings from the harness).

One more check: visibility of the pendulum — with pivot at H*0.36 and scale min(W,H)/5.2 = 620/5.2 ≈ 119.2 px/unit, the reach range is 2 units = 238 px. Pivot y = 223; max downward y = 223+238=461 < 620; max upward = 223-238 = -15 — slightly above the top edge of the canvas when fully inverted! In frame 4 of the motion capture, the lower bob reached near the top (y≈250 in screenshot coordinates, no problem). If both rods point straight up, bob 2 would be at y=-15, off-canvas. That's an extreme configuration; with this energy (E0=0.149), can bob 2 reach full inversion above the pivot? Max height of bob 2: PE_max when both point up = (M1+M2)*G*L1 + M2*G*L2 = 3*9.81 = 29.43 >> E0. But bob 2 alone pointing up while bob 1 points down: PE = -(M1+M2)G L1 cos(0)... wait, PE = -(M1+M2) G L1 cos t1 - M2 G L2 cos t2. With t1=0 (down), t2=π (up): PE = -19.62 + 9.81 = -9.81 < E0=0.149. So bob 2 can pass over the top while bob 1 points down — in that case bob 2's y = pivot_y + SCALE*(cos t1 + cos t2) = 223 + 119*(1-1)=223. No problem. Worst case for on-screen visibility: maximize upward reach: y2 = PY + SCALE*(cos t1 + cos t2), minimum when both cos = -1 → y2 = 223 - 238 = -15. PE in that configuration = +29.43 > E0, unreachable. Reachable extremes: cos t1 + cos t2 subject to PE ≤ E0: -(2 cos t1 + cos t2)*9.81 ≤ 0.149 → 2cos t1 + cos t2 ≥ -0.0152. Minimize c = cos t1 + cos t2 subject to 2cos t1 + cos t2 ≥ -0.0152: set cos t2 = -0.0152 - 2cos t1; c = cos t1 - 0.0152 - 2 cos t1 = -cos t1 - 0.0152, minimized at cos t1 = 1 → c = -1.0152? But cos t2 = -0.0152-2 = -2.0152 is invalid. Constraint cos t2 ≥ -1: -0.0152 - 2cos t1 ≥ -1 → cos t1 ≤ 0.4924. Then c = -cos t1 - 0.0152 ≥ -0.5076. So y2 ≥ 223 - 119*... wait, c = cos t1 + cos t2 ≥ -0.5076 → y2 ≥ 223 + 119.2*(-0.5076) ≈ 223 - 60.5 = 162.5. Well inside the canvas. And the bob's radius etc. are also fine. Also x range: |x2 - PX| ≤ SCALE*2 = 238 < 360. Good — always visible.

Also trail bounds: points are within the canvas. Good.

Everything verified. Done. Report.