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Lie group integrator

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1199: 25: 143: 1159: 350: 1154: 1240: 441: 465: 660: 256: 530: 756: 809: 337: 1259: 1093: 181:; Marthinsen, Håkon; Owren, Brynjulf (2012). "An introduction to Lie group integrators -- basics, new developments and applications". 61: 43: 858: 121: 450: 1233: 841: 1053: 1038: 761: 535: 1264: 1083: 1226: 1088: 1058: 766: 722: 703: 470: 414: 625: 490: 1010: 875: 567: 409: 148: 153: 707: 677: 601: 591: 547: 377: 330: 114: 475: 1048: 667: 562: 382: 158: 302: 697: 692: 86: 79: 1028: 966: 814: 518: 508: 480: 455: 365: 200: 1206: 1166: 1139: 848: 726: 711: 640: 399: 1108: 1063: 960: 831: 635: 460: 323: 284: 216: 190: 98: 645: 1043: 1023: 1018: 925: 836: 650: 630: 485: 424: 276: 133: 106: 1181: 975: 930: 853: 824: 682: 615: 610: 605: 595: 387: 370: 268: 235:"AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL" 208: 90: 82: 1124: 1033: 863: 819: 585: 252: 234: 178: 204: 1210: 990: 915: 885: 783: 776: 716: 687: 557: 552: 513: 110: 1253: 1176: 1000: 995: 980: 970: 920: 897: 771: 731: 672: 620: 419: 288: 220: 1103: 1098: 940: 907: 880: 788: 429: 118: 1198: 946: 935: 892: 793: 394: 1171: 1129: 955: 868: 500: 404: 272: 212: 280: 985: 950: 655: 542: 138: 1149: 1144: 1134: 525: 346: 94: 315: 117:
research. These tasks are particularly difficult because they feature
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provides insufficient context for those unfamiliar with the subject
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Method of numerical integration of partial differential equations
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Iserles, Arieh; Munthe-Kaas, Hans Z.; Nørsett, Syvert P.;
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Numerical methods for ordinary differential equations
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built from coordinate-independent operations such as
1117: 1076: 1009: 906: 802: 749: 740: 576: 499: 438: 358: 1234: 331: 8: 1241: 1227: 746: 338: 324: 316: 194: 62:Learn how and when to remove this message 170: 44:providing more context for the reader 7: 1195: 1193: 14: 1197: 183:Journal of Computational Physics 23: 378:Differentiable/Smooth manifold 97:. They have been used for the 1: 1213:. You can help Knowledge by 1084:Classification of manifolds 1281: 1192: 1260:Applied mathematics stubs 1160:over commutative algebras 273:10.1017/S0962492900002154 213:10.1016/j.jcp.2012.12.031 876:Riemann curvature tensor 149:Parallel parking problem 115:artificial intelligence 1209:-related article is a 668:Manifold with boundary 383:Differential structure 159:Variational integrator 87:differential equations 80:numerical integration 815:Covariant derivative 366:Topological manifold 76:Lie group integrator 1207:applied mathematics 849:Exterior derivative 451:Atiyah–Singer index 400:Riemannian manifold 257:"Lie-group methods" 205:2014JCoPh.257.1040C 189:(2014): 1040–1061. 154:Runge–Kutta methods 40:improve the article 1265:Numerical analysis 1155:Secondary calculus 1109:Singularity theory 1064:Parallel transport 832:De Rham cohomology 471:Generalized Stokes 1222: 1221: 1190: 1189: 1072: 1071: 837:Differential form 491:Whitney embedding 425:Differential form 134:Euler integration 107:computer graphics 91:Lie group actions 72: 71: 64: 1272: 1243: 1236: 1229: 1201: 1194: 1182:Stratified space 1140:Fréchet manifold 854:Interior product 747: 444: 340: 333: 326: 317: 310: 309: 307: 299: 293: 292: 253:Zanna, Antonella 248: 242: 241: 239: 231: 225: 224: 198: 179:Celledoni, Elena 175: 67: 60: 56: 53: 47: 27: 26: 19: 1280: 1279: 1275: 1274: 1273: 1271: 1270: 1269: 1250: 1249: 1248: 1247: 1191: 1186: 1125:Banach manifold 1118:Generalizations 1113: 1068: 1005: 902: 864:Ricci curvature 820:Cotangent space 798: 736: 578: 572: 531:Exponential map 495: 440: 434: 354: 344: 314: 313: 305: 301: 300: 296: 250: 249: 245: 237: 233: 232: 228: 177: 176: 172: 167: 130: 111:control systems 101:and control of 68: 57: 51: 48: 37: 28: 24: 17: 12: 11: 5: 1278: 1276: 1268: 1267: 1262: 1252: 1251: 1246: 1245: 1238: 1231: 1223: 1220: 1219: 1202: 1188: 1187: 1185: 1184: 1179: 1174: 1169: 1164: 1163: 1162: 1152: 1147: 1142: 1137: 1132: 1127: 1121: 1119: 1115: 1114: 1112: 1111: 1106: 1101: 1096: 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852: 850: 847: 843: 842:Vector-valued 840: 839: 838: 835: 833: 830: 826: 823: 822: 821: 818: 816: 813: 811: 808: 807: 805: 801: 795: 792: 790: 787: 785: 782: 778: 775: 774: 773: 772:Tangent space 770: 768: 765: 763: 760: 758: 755: 754: 752: 748: 745: 743: 739: 733: 730: 728: 724: 720: 718: 715: 713: 709: 705: 701: 699: 696: 694: 691: 689: 686: 684: 681: 679: 676: 674: 671: 669: 666: 662: 659: 658: 657: 654: 652: 649: 647: 644: 642: 639: 637: 634: 632: 629: 627: 624: 622: 619: 617: 614: 612: 609: 607: 603: 599: 597: 593: 589: 587: 584: 583: 581: 575: 569: 566: 564: 561: 559: 556: 554: 551: 549: 546: 544: 541: 537: 536:in Lie theory 534: 533: 532: 529: 527: 524: 520: 517: 516: 515: 512: 510: 507: 506: 504: 502: 498: 492: 489: 487: 484: 482: 479: 477: 474: 472: 469: 467: 464: 462: 459: 457: 454: 452: 449: 448: 446: 443: 439:Main results 437: 431: 428: 426: 423: 421: 420:Tangent space 418: 416: 413: 411: 408: 406: 403: 401: 398: 396: 393: 389: 386: 384: 381: 380: 379: 376: 372: 369: 368: 367: 364: 363: 361: 357: 352: 348: 341: 336: 334: 329: 327: 322: 321: 318: 304: 298: 295: 290: 286: 282: 278: 274: 270: 266: 262: 261:Acta Numerica 258: 254: 247: 244: 236: 230: 227: 222: 218: 214: 210: 206: 202: 197: 192: 188: 184: 180: 174: 171: 164: 160: 157: 155: 152: 150: 147: 145: 142: 140: 137: 135: 132: 131: 127: 125: 123: 120: 116: 112: 108: 104: 100: 96: 92: 88: 84: 81: 77: 66: 63: 55: 45: 41: 35: 32:This article 30: 21: 20: 1215:expanding it 1204: 1104:Moving frame 1099:Morse theory 1089:Gauge theory 881:Tensor field 810:Closed/Exact 789:Vector field 757:Distribution 698:Hypercomplex 693:Quaternionic 430:Vector field 388:Smooth atlas 297: 264: 260: 246: 229: 186: 182: 173: 119:nonholonomic 75: 73: 58: 49: 38:Please help 33: 1049:Levi-Civita 1039:Generalized 1011:Connections 961:Lie algebra 893:Volume form 794:Vector flow 767:Pushforward 762:Lie bracket 661:Lie algebra 626:G-structure 415:Pushforward 395:Submanifold 267:: 215–365. 122:constraints 1254:Categories 1172:Stratifold 1130:Diffeology 926:Associated 727:Symplectic 712:Riemannian 641:Hyperbolic 568:Submersion 476:Hopf–Rinow 410:Submersion 405:Smooth map 165:References 52:March 2017 1054:Principal 1029:Ehresmann 986:Subbundle 976:Principal 951:Fibration 931:Cotangent 803:Covectors 656:Lie group 636:Hermitian 579:manifolds 548:Immersion 543:Foliation 481:Noether's 466:Frobenius 461:De Rham's 456:Darboux's 347:Manifolds 289:121539932 281:1474-0508 196:1207.0069 139:Lie group 99:animation 1150:Orbifold 1145:K-theory 1135:Diffiety 859:Pullback 673:Oriented 651:Kenmotsu 631:Hadamard 577:Types of 526:Geodesic 351:Glossary 221:28406272 128:See also 103:vehicles 95:manifold 1094:History 1077:Related 991:Tangent 969:)  949:)  916:Adjoint 908:Bundles 886:density 784:Torsion 750:Vectors 742:Tensors 725:)  710:)  706:,  704:Pseudo− 683:Poisson 616:Finsler 611:Fibered 606:Contact 604:)  596:Complex 594:)  563:Section 201:Bibcode 1059:Vector 1044:Koszul 1024:Cartan 1019:Affine 1001:Vector 996:Tensor 981:Spinor 971:Normal 967:Stable 921:Affine 825:bundle 777:bundle 723:Almost 646:Kähler 602:Almost 592:Almost 586:Closed 486:Sard's 442:(list) 287:  279:  219:  83:method 1205:This 1167:Sheaf 941:Fiber 717:Rizza 688:Prime 519:Local 509:Curve 371:Atlas 306:(PDF) 285:S2CID 238:(PDF) 217:S2CID 191:arXiv 93:on a 78:is a 1211:stub 1034:Form 936:Dual 869:flow 732:Tame 708:Sub− 621:Flat 501:Maps 277:ISSN 109:and 85:for 956:Jet 269:doi 209:doi 187:257 105:in 42:by 1256:: 947:Co 283:. 275:. 263:. 259:. 215:. 207:. 199:. 185:. 124:. 74:A 1242:e 1235:t 1228:v 1217:. 965:( 945:( 721:( 702:( 600:( 590:( 353:) 349:( 339:e 332:t 325:v 308:. 291:. 271:: 265:9 240:. 223:. 211:: 203:: 193:: 113:/ 65:) 59:( 54:) 50:( 46:. 36:.

Index

improve the article
providing more context for the reader
Learn how and when to remove this message
numerical integration
method
differential equations
Lie group actions
manifold
animation
vehicles
computer graphics
control systems
artificial intelligence
nonholonomic
constraints
Euler integration
Lie group
Numerical methods for ordinary differential equations
Parallel parking problem
Runge–Kutta methods
Variational integrator
Celledoni, Elena
arXiv
1207.0069
Bibcode
2014JCoPh.257.1040C
doi
10.1016/j.jcp.2012.12.031
S2CID
28406272

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