Double pendulum · mercury-3
Output saved · Timed out Cost / run $0.0374 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.
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 · 48 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.
/tmp/job-VESk6O/index.html (9439 bytes)Successfully wrote to /tmp/job-VESk6O/index.html
Now let me verify the physics off-line (energy conservation over a long simulation) before running in the browser.
{"command":"cd /tmp/job-VESk6O && python3 - <<'EOF'\nimport math\nG=9.81; L=1; M=1\nth1=120*math.pi/180; th2=-10*math.pi/180; w1=0.0; w2=0.0/bin/bash: line 1: python3: command not found Command exited with code 127
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81, L=1, M=1;\nlet th1=120*Math.PI/180, th2=-10*Math.PI/180, w1=0, w2=0;\nfunctit=0.001s θ1=119.99971301212167 θ2=349.99986432967506 w1=-0.01001776463468466 w2=-0.004735766354270212 E=0.14898576514609507 t=5.001s θ1=334.0665610967578 θ2=43.10726230493606 w1=-3.46692509299966 w2=-3.995281658003308 E=-5.860748859162751 t=50.001s θ1=60.756230614674905 θ2=358.950912680666 w1=-4.609792895425033 w2=1.0256859517953225 E=-10.4760593418262 t=120.000s θ1=286.2485062215415 θ2=104.5809749010566 w1=-0.23632190485312077 w2=-2.7426911930728597 E=0.12111185966528204 E0=0.14903594295023498, max|E-E0| over 120s = 28.630704158439862
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\n// Wikipedia formula (m1=m2=1,L1=L2=1)\nfunction wiki(a1,a2,c1,c2){\n consmax |wiki - matrix| = 2.842170943040401e-14
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, den=3-Math.cos(2*d);\n conh=0.001 E0=0.149036 maxdev over 3s=2.644e+1 EndE=-0.140540 h=0.0001 E0=0.149036 maxdev over 3s=2.736e+1 EndE=-0.140540 h=0.00002 E0=0.149036 maxdev over 3s=2.740e+1 EndE=-0.140540
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, den=3-Math.cos(2*d);\n conworst |dE/dt| = 1111.3423793012776 plain pendulum check at a=1.0,c=0.5: 0.5 expected -8.254830360965466
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction energy(a1,a2,c1,c2){ return 0.5*(c1*c1+c2*c2+2*c1*c2*Math.cos(a1-agrad[0] analytic=8.11789369293908 numeric=8.117894587655883 diff=-8.947168019801666e-7 grad[1] analytic=10.431738807813872 numeric=10.43173906367656 diff=-2.5586268748156726e-7 grad[2] analytic=1.2351578127155114 numeric=1.2351578604352653 diff=-4.771975392614536e-8 grad[3] analytic=0.529684374568977 numeric=0.529684420769172 diff=-4.620019500300998e-8
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, den=3-Math.cos(2*d);\n converlet h=1e-4 over 3s: { E0: 0.14903594295023498, maxdev: 27.396008002935822, EndE: -0.15771628143244953 } verlet h=1e-5 over 3s: { E0: 0.14903594295023498, maxdev: 27.396610448256098, EndE: -0.142193738168098 } A1,A2 at start = -10.017768922254366 -4.735809117015397 dE/dt at start (c1=c2=0 => 0) OK dE/dt at state = -0.28546986831455534
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction L(a1,a2,c1,c2){\n const T=0.5*(c1*c1+c2*c2+2*c1*c2*Math.cos(a1-a2worst |generic - closedform| = 10872924715158636 at state: {"a1":-0.10394046337045862,"a2":3.036696166793058,"c1":6.69166263505617,"c2":-3.9704774557599425,"g":[-130426182.45858763,10872924715158636],"f":[0.980755294258409,-0.08920274666734475]}
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction L(q,v){ // q=[a1,a2], v=[c1,c2]\n const d=q[0]-q[1];\n const T=0state [2.094,-0.175,0,0] gen=[-11.322102,0.057889] cf=[-10.017769,-4.735809] state [0.5,1.2,2,-1] gen=[20.68276,-20.683811] cf=[0.142735,-11.829344] state [1,2,5,3] gen=[-33.648556,33.64835] cf=[4.2442,-32.250133] state [-1,0.3,-4,6] gen=[71.661838,-71.661302] cf=[29.089384,-26.09736]
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction L(q,v){ const d=q[0]-q[1];\n return 0.5*(v[0]*v[0]+v[1]*v[1]+2*v[aligned AD: [ -Infinity, Infinity ] expected -8.254830360965466 aligned AD rest: [ -Infinity, Infinity ] expected -8.254830360965466 initial state AD: [ -27.088930450270624, -15.708940154299277 ]
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, den=3-Math.cos(2*d);\n conmild 10°,5° h=1e-5 5s: { E0: -29.094598102379546, maxdev: 0.18305072618716878, EndE: -29.145247791164028 } mild 10°,5° h=1e-3 5s: { E0: -29.094598102379546, maxdev: 0.1829735468110485, EndE: -29.145247791141443 } wild 120°,-10° h=1e-5 0.5s: { E0: 0.14903594295023498, maxdev: 13.121998682253446, EndE: -12.994323647667876 } wild 120°,-10° h=1e-5 1.0s: { E0: 0.14903594295023498, maxdev: 27.396496577330904, EndE: -1.8041327950456125 } wild 120°,-10° h=1e-5 2.0s: { E0: 0.14903594295023498, maxdev: 27.396496577330904, EndE: 0.14742983111109353 }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction L(q,v){ const d=q[0]-q[1];\n return 0.5*(v[0]*v[0]+v[1]*v[1]+2*v[M= [ [ 1, 0.764842 ], [ 0.764842, 1 ] ] C= [ [ -0.644218, 1.288436 ], [ 0.644218, -1.288435 ] ] g= [ -10.694764, -7.854868 ] closed A=[ 0.142735 , -11.829344 ] residual=[ -0.786952 , -1.288432 ]
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\n// Corrected closed form derived from M,C,g structure\nfunction derivs2(a1,state [2.094,-0.175,0,0] gen=[-27.0889,-15.7089] new=[-27.0889,-15.7089] state [0.5,1.2,2,-1] gen=[-0.3355,-10.1751] new=[-11.2936,0.783] state [1,2,5,3] gen=[-43.9669,27.4573] new=[-9.1877,-7.322] state [-1,0.3,-4,6] gen=[50.1877,-39.4496] new=[-23.4766,34.2148] state [0.3,0.8,1,0.5] gen=[-0.315,-6.5211] new=[-4.2313,-2.6048] worst dev = 73.66437554790491
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs3(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=Math.cos(state [2.094,-0.175,0,0] gen=[-27.0889,-15.7089] new=[-27.0889,-15.7089] state [0.5,1.2,2,-1] gen=[-0.3355,-10.1751] new=[-0.3356,-10.1751] state [1,2,5,3] gen=[-43.9669,27.4573] new=[-43.967,27.4573] state [-1,0.3,-4,6] gen=[50.1877,-39.4496] new=[50.1878,-39.4496] state [0.3,0.8,1,0.5] gen=[-0.315,-6.5211] new=[-0.315,-6.5211] worst dev = 0.000058549555436826495
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=Math.cos(dmild 10°,5° h=1e-5 5s: { E0: -29.094598102379546, maxdev: NaN, EndE: NaN, minsin: NaN } mild 10°,5° h=1e-3 5s: { E0: -29.094598102379546, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=1e-5 10s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=1e-3 10s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=0.5e-3 60s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=Math.cos(dmild 10°,5° h=1e-5 5s: { E0: -29.094598102379546, maxdev: NaN, EndE: NaN, minsin: NaN } mild 10°,5° h=1e-3 5s: { E0: -29.094598102379546, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=1e-5 10s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=1e-3 10s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN } wild 120°,-10° h=0.5e-3 60s: { E0: 0.14903594295023498, maxdev: NaN, EndE: NaN, minsin: NaN }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=Math.cos(dE0 0.14903594295023498 0 k1 [ 0, 0, -27.0889, -15.7089 ] k4 [ -0.0003, -0.0002, -27.0889, -15.7089 ] s [ 2.0944, -0.1745, -0.0003, -0.0002 ] E 0.1490359429502385 1 k1 [ -0.0003, -0.0002, -27.0889, -15.7089 ] k4 [ -0.0005, -0.0003, -27.0889, -15.7089 ] s [ 2.0944, -0.1745, -0.0005, -0.0003 ] E 0.1490359429502403 2 k1 [ -0.0005, -0.0003, -27.0889, -15.7089 ] k4 [ -0.0008, -0.0005, -27.0889, -15.7089 ] s [ 2.0944, -0.1745, -0.0008, -0.0005 ] E 0.1490359429502427 3 k1 [ -0.0008, -0.0005, -27.0889, -15.7089 ] k4 [ -0.0011, -0.0006, -27.0889, -15.7089 ] s [ 2.0944, -0.1745, -0.0011, -0.0006 ] E 0.1490359429502436 4 k1 [ -0.0011, -0.0006, -27.0889, -15.7089 ] k4 [ -0.0014, -0.0008, -27.0889, -15.7089 ] s [ 2.0944, -0.1745, -0.0014, -0.0008 ] E 0.1490359429502421
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=Math.cos(dNaN at i=908 k1= [ Infinity, -Infinity, NaN, NaN ] prev s= [ NaN, NaN, NaN, NaN ] { E0: 0.14903594295023498, maxdev: 0.21498605622968742, EndE: NaN, minsin: 0.0002733712972249634 }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81, REG=1e-4;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=DT=1e-3, 10s: { E0: 0.14903594295023498, maxdev: 0.08503421109338821, EndE: NaN, fail: true, i: 1286 } DT=1e-3, 120s: { E0: 0.14903594295023498, maxdev: 0.08503421109338821, EndE: NaN, fail: true, i: 1286 } DT=1e-3, 600s: { E0: 0.14903594295023498, maxdev: 0.08503421109338821, EndE: NaN, fail: true, i: 1286 }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81, REG=1e-4, AMAX=2000;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=MathDT=1e-3 30s: { E0: 0.14903594295023498, maxdev: 224.95879070409657, EndE: 192.03305756717373, fail: false, w1: -36.15333321924976, w2: -21.422411382389, minsin: 0.00001190625424700311 } DT=1e-3 300s: { E0: 0.14903594295023498, maxdev: 661.3490402208789, EndE: 32.52081474671579, fail: false, w1: 20.14513192416724, w2: 14.23953891393242, minsin: 0.000007783507148030729 } DT=1e-3 1200s: { E0: 0.14903594295023498, maxdev: 724.4117450517665, EndE: 174.866989011139, fail: false, w1: 28.15159212507503, w2: 46.28431769499039, minsin: 4.849339259619927e-7 }
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81, REG=1e-6, AMAX=1e6;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.DT=1e-4 60s: { E0: 0.14903594295023498, maxdev: 450.23319442244934, EndE: 237.68635568056274, fail: false, w1: -3795.34313449087, w2: -3815.164521613653, minsin: 2.5740600394597985e-8 } DT=1e-4 600s: { E0: 0.14903594295023498, maxdev: 33480.348631348075, EndE: 396.3730043899815, fail: false, w1: -11537.931714790211, w2: -11543.208882211398, minsin: 1.7308497624944552e-9 } DT=1e-4 1800s: { E0: 0.14903594295023498, maxdev: 33480.348631348075, EndE: 542.9851973404212, fail: false, w1: -17452.989023527396, w2: -17425.31789025196, minsin: 1.4980191188405856e-9 }
10 minutes have elapsed. At most 5 minutes remain. Finalize the output as soon as possible: save index.html now, fix only essential issues, and finish.
{"command":"cd /tmp/job-VESk6O && node - <<'EOF'\nconst G=9.81, REG=1e-4;\nfunction derivs(a1,a2,c1,c2){\n const d=a1-a2, s=Math.sin(d), c=