Double pendulum · kimi-k3.1-pro

I need build. Should inspect files.

Should design polished simulation, accurate coupled RK4 substep. Self-contained no external. Canvas responsive, controls pause reset, perhaps trail toggle? Required only. I can add energy display, speed selection? Keep functionality focused. Make sure initial angles 120 and -10 measured downward vertical, equal lengths/masses, g 9.81 consistent simulation units. Use L=1.5m perhaps scaled. Physics acceleration formula for equal masses:
dtheta1=omega1 etc
den = 2m1+m2 - m2 cos(2theta1-2theta2)
a1 = [-g(2m1+m2) sinθ1 - m2 g sin(θ1-2θ2) -2 sin(θ1-θ2)m2(ω2² L2 + ω1²L1 cos(θ1-θ2))]/(L1 den)
a2 = [2 sin(θ1-θ2)(ω1² L1(m1+m2)+g(m1+m2) cosθ1+ω2² L2 m2 cos(θ1-θ2))]/(L2 den)
m1=m2. Good.

RK4 fixed 1/480 sec or frame time / 8. Could use accumulator fixed dt=1/480 cap elapsed 0.05 prevents leaps. Time scale 1. Use canvas DPR. Trail bounded array max 1800 points with time, perhaps drawn segmented fading alpha and hue. Colorful fading trail using hue over time, alpha proportional age and index. Should visually excellent: dark navy backdrop grid/space, glass panel controls, energy etc. Single-page canvas occupies entire card. Header with icon, label "DOUBLE PENDULUM" / "Chaos in motion"; pause button top? Footer status. Trail should be obvious.

Should trail under rods, colorful fading, lower bob glows. Add "CLEAR TRAIL"? Not needed perhaps Reset clears. Show theta readouts with deg, ω; energy. A small legend "Equal masses · Equal rods · No damping". Pause freezes simulation and no trail changes (redraw okay same trail). Reset sets t=0 initial and trail initialized perhaps lower bob position; cleared trail means no previous. Clear trail [] or [initial]? Verify screenshot reset starting pose cleared trail. Better [] and draw no trail until movement. Status. Canvas interactive? Could support keyboard Space/R. Not asked but good.

Implement fixed pivot centered horizontally at perhaps y 32% of canvas. Scale must keep visible all possible lower bob within 2L circle. Scale = min(width*0.18, height*0.25?) Should screen coordinates rod length = min(width/(2*L*1.25), height/(2*L*1.25)) times L. Pivot y=height*0.35 perhaps lower bob can below pivot by 2 rods => pivotY +2 rod <= height-30; above pivot by2 rods >=20. Choose scale=min(width*0.36? single length pixel = width*0.21 perhaps, height*0.25?) If pivot y=height*0.34, top clearance height*.34-20 /2; bottom height*.66-30 /2. lengthPixels=min(width*.22,(height*.34-25)/2,(height*.66-35)/2). For 900x600 canvas length ~153; lower spans306, pivot204, bottom510 good. For 1200x? likely. Should panel header outside canvas perhaps layout 100vh; sidebar? I can make card max-width 1100 height calc(100vh - 64px) min-height 580. Canvas flexible. Body with header title and toolbar top, simulation canvas fills. Stats bottom. On 1200x800 good.

Could place canvas background with generated static stars? Physics scientific feel. No assets. CSS gradients allowed. Draw subtle grid in canvas. Bounded fading trail 1600 samples at 120Hz perhaps max13 sec. Fading age 9s plus cap. Better trail points per fixed substep at 120Hz (every 4 RK4) to avoid huge. Trail max 1600 and life=10 seconds; bounded both count and age. Each point {x,y,t,hue}; x,y model positions or canvas coordinates? On resize if pixels old wrong. Store physical x,y (units L* sin etc). Convert each draw. Lower bob x=L(sinθ1+sinθ2), y=L(cosθ1+cosθ2). Draw segments between consecutive points only if adjacent time <.1? At reset clear. Fade based age (t current - p.t), alpha=(1-age/life)^1.5 *0.8. Hue=(p.t*45 + 190)%360 perhaps vivid cyan-purple-pink. Segment each draw 1200 * line strokes expensive but okay. Use grouped by age/hue? Each segment individual to hue fade. 1200 at60fps okay. Draw glow perhaps just main. Could draw old segments lineWidth1.4 to3.0 recent. globalCompositeOperation='lighter'. Trail colorful. Store point every fixed step 1/240, max2400 life10 =2400 potentially heavy. dt=1/480 and sample every4 =120 Hz life9 =1080. Good. Initial fast trail perhaps appears.

Energy display compute kinetic and potential to assure. Equal masses. T=0.5 m L² ω1² +0.5mL²(ω1²+ω2²+2ω1ω2cosΔ) = mL²ω1² +.5mL²ω2² +mL²ω1ω2cosΔ. V=-m g L cosθ1 -mgL(cosθ1+cosθ2)= -mgL(2cosθ1+cosθ2). total. Baseline E0 display drift (E-E0) perhaps in millijoules. Stats θ1 θ2 and time. Energy perhaps shows E total with sign, not intuitive. "Energy drift +0.000%" useful stable. dt note.

Numerical energy RK4 may slowly drift but good. At initial angles 120 and -10 energies near? no issue.

Should accessible responsive, button text. I'll write.

Now run browser inspect.

Looks tiny pendulum because rodPixels min bottom room/2 ~? stage height600 pivot210 bottom356/2=178 but screenshot rods85? Wait canvas CSS width/height weird resize loops? screenshot upper-to-lower 86, pivot to upper85. Formula topRoom180/2=90. pivot at210, top boundary30; to keep upward2rod pivot-180=30. yes rod=90. Lower max bottom570. Pendulum appears small center with huge stage. Could enlarge by shift pivot to center y .5 and rod min (h/2-30)/2 =135. Current .35 limits top. Should better visual size perhaps pivot 0.46 giving 126, total252. At initial upper bob y=~170 lower=~290, good. Current rods 90 tiny. Want 145 with pivot .5. Stage600, top room270/2=135 bottom room266/2=133. ~133. Still moderate. screenshot stage600. 2rod266, fills44% height. good. Current180 only30%. Set pivot .47 top252/2=126 bottom284/2=142 =>126. width allows245. Fine. Perhaps 140 by .5. Full lower reach almost canvas all. Keep visible 34 margin. use .48 -> top258/2=129, bottom278/2=139. okay.

Trail at initial no chaotic movement early. Now sample several moments. Browser screenshot after some seconds.

Motion good. Trail looks not fading? yes. Could enlarge 1.4. At time12 lower reached y273 pivot317 diff-44 because angle etc. With max envelope okay. Set pivot .46? Current pivot y317. stage top107 height600 pivot .35=317. To enlarge pivot center y407, rods 129, bottom full reach665 stage bottom707 with42 margin. Good. Use .5 gives equal. initial upper bob y? θ1 120 cos=-.5 upper y+rod/2=471; lower y+rod cos-10 ~598, near bottom. Reset initial lower near bottom. Current initial lower at410. With center, lower 407+64+127=598 stage bottom707 =109 margin. Fine. Motion upper can up to145. Good. scale129. set .5. Visually fills much better. Envelope circle radius258 centered407 reaches149 to665. Fine.

Now test pause. Click at current and inspect twice to confirm.

Looks good bigger. Now pause inspect.

Angle θ2 416° physically okay but readout perhaps angles should normalize for readable. Not requirement. Could normalize [-180,180], avoids weird 416. Starting still. Better signedDegrees normalize to (-180,180] display. Angles from vertical perhaps expected. Use normalized. Also pivot label? no.

Check pause with inspect after wait tool perhaps inspect takes instant but dom same.

Good. Resume then reset.

Resume works. Reset and pause immediately? Requirement reset restores initial conditions and clears trail. If running, screenshot after reset at 0.1 angles differ. Verification might click reset and expect exactly120 -10. User may expect simulation restarts moving, normal. To confirm immediate browser result may show 0.08. Could reset preserve pause state. Currently if paused, reset remains paused exactly initial. If running resets and runs. Good. Test reset while paused to show exact. Click pause then reset. But first normalize.

Potential equations correctness. I'll verify formula a1 equal masses standard:
a1 = (-g(2m1+m2)sinθ1 -m2g sin(θ1-2θ2) -2 sinΔ m2(ω2²L2 +ω1²L1 cosΔ))/(L1(2m1+m2-m2 cos2Δ)) = -3g sin a -g sin(a-2b)-2sd(v²L+u²Lcd) yes.
a2 numerator 2sd( u²L1(m1+m2)+g(m1+m2)cos a +v²L2m2cd) =2sd(2u²L+2gcos a+v²Lcd). yes.

Conservation display 0.000 could hide small drift but good.

Time tool actual sim runs much faster than real? Browser calls tool taking6 sec etc. Fine.

Perhaps ensure no ResizeObserver loop due setting canvas style widths same. okay.

Mobile responsive possible rodPixels calculation min max. Height under low screen app min height0 at maxheight560. pivot etc. topRoom max20 can rod min20. visible. Good.

One issue Trail clearing reset draw after running immediate next frame adds after 1/120 sec. "clears trail" yes previous gone.

I'll reset screenshot paused exact.

Perhaps perhaps browser screenshot after 0.3 but image 0.12. okay.

Click pause/reset.

All. But requirement "Keep both rod lengths constant and pendulum visible" yes geometry from trig constant. Trail bounded 1200 and age10. Numerical stable fixed dt. Good.

Perhaps check resume after reset to ensure starting. Already did earlier. Console clear. Respond concise report with verified and unverified. User asks build not explanation. mention index.html. Could say verified sampled motion, connected rods, fading trail; pause/resume; paused reset exact. Remaining unverified long-duration numerical behavior/mobile layouts? I did only brief. I'll explicitly note which remain unverified. "Long-run behavior beyond sampled playback was not exhaustively tested." Could mention responsive not checked. No need more tools.

But perhaps I should ensure file present. yes. Respond.