1210:
36:
154:
1170:
361:
1165:
1251:
452:
476:
671:
267:
541:
767:
54:
820:
348:
1270:
1104:
192:; Marthinsen, Håkon; Owren, Brynjulf (2012). "An introduction to Lie group integrators -- basics, new developments and applications".
72:
869:
132:
461:
1244:
852:
1064:
1049:
772:
546:
1275:
1094:
1237:
1099:
1069:
777:
733:
714:
481:
425:
636:
501:
1021:
886:
578:
420:
159:
164:
718:
688:
612:
602:
558:
388:
341:
125:
486:
1059:
678:
573:
393:
169:
313:
708:
703:
97:
90:
1039:
977:
825:
529:
519:
491:
466:
376:
211:
1217:
1177:
1150:
859:
737:
722:
651:
410:
1119:
1074:
971:
842:
646:
471:
334:
295:
227:
201:
109:
656:
1054:
1034:
1029:
936:
847:
661:
641:
496:
435:
287:
144:
117:
1221:
1192:
986:
941:
864:
835:
693:
626:
621:
616:
606:
398:
381:
279:
246:"AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL"
219:
101:
93:
1135:
1044:
874:
830:
596:
263:
245:
189:
215:
1001:
926:
896:
794:
787:
727:
698:
568:
563:
524:
121:
1264:
1187:
1011:
1006:
991:
981:
931:
908:
782:
742:
683:
631:
430:
299:
17:
231:
1114:
1109:
951:
918:
891:
799:
440:
129:
1209:
957:
946:
903:
804:
405:
1182:
1140:
966:
879:
511:
415:
283:
223:
291:
996:
961:
666:
553:
149:
1160:
1155:
1145:
536:
357:
105:
326:
128:
research. These tasks are particularly difficult because they feature
113:
752:
45:
provides insufficient context for those unfamiliar with the subject
206:
314:"Lie Group Integrators for the animation and control of vehicles"
27:
Method of numerical integration of partial differential equations
330:
29:
262:
Iserles, Arieh; Munthe-Kaas, Hans Z.; Nørsett, Syvert P.;
1225:
50:
155:
Numerical methods for ordinary differential equations
100:
built from coordinate-independent operations such as
1128:
1087:
1020:
917:
813:
760:
751:
587:
510:
449:
369:
1245:
342:
8:
1252:
1238:
757:
349:
335:
327:
205:
73:Learn how and when to remove this message
181:
55:providing more context for the reader
7:
1206:
1204:
1224:. You can help Knowledge (XXG) by
25:
1208:
194:Journal of Computational Physics
34:
389:Differentiable/Smooth manifold
108:. They have been used for the
1:
1095:Classification of manifolds
1292:
1203:
1271:Applied mathematics stubs
1171:over commutative algebras
284:10.1017/S0962492900002154
224:10.1016/j.jcp.2012.12.031
887:Riemann curvature tensor
160:Parallel parking problem
126:artificial intelligence
1220:-related article is a
679:Manifold with boundary
394:Differential structure
170:Variational integrator
98:differential equations
91:numerical integration
18:Lie group integrators
826:Covariant derivative
377:Topological manifold
87:Lie group integrator
1218:applied mathematics
860:Exterior derivative
462:Atiyah–Singer index
411:Riemannian manifold
268:"Lie-group methods"
216:2014JCoPh.257.1040C
200:(2014): 1040–1061.
165:Runge–Kutta methods
51:improve the article
1276:Numerical analysis
1166:Secondary calculus
1120:Singularity theory
1075:Parallel transport
843:De Rham cohomology
482:Generalized Stokes
1233:
1232:
1201:
1200:
1083:
1082:
848:Differential form
502:Whitney embedding
436:Differential form
145:Euler integration
118:computer graphics
102:Lie group actions
83:
82:
75:
16:(Redirected from
1283:
1254:
1247:
1240:
1212:
1205:
1193:Stratified space
1151:Fréchet manifold
865:Interior product
758:
455:
351:
344:
337:
328:
321:
320:
318:
310:
304:
303:
264:Zanna, Antonella
259:
253:
252:
250:
242:
236:
235:
209:
190:Celledoni, Elena
186:
78:
71:
67:
64:
58:
38:
37:
30:
21:
1291:
1290:
1286:
1285:
1284:
1282:
1281:
1280:
1261:
1260:
1259:
1258:
1202:
1197:
1136:Banach manifold
1129:Generalizations
1124:
1079:
1016:
913:
875:Ricci curvature
831:Cotangent space
809:
747:
589:
583:
542:Exponential map
506:
451:
445:
365:
355:
325:
324:
316:
312:
311:
307:
261:
260:
256:
248:
244:
243:
239:
188:
187:
183:
178:
141:
122:control systems
112:and control of
79:
68:
62:
59:
48:
39:
35:
28:
23:
22:
15:
12:
11:
5:
1289:
1287:
1279:
1278:
1273:
1263:
1262:
1257:
1256:
1249:
1242:
1234:
1231:
1230:
1213:
1199:
1198:
1196:
1195:
1190:
1185:
1180:
1175:
1174:
1173:
1163:
1158:
1153:
1148:
1143:
1138:
1132:
1130:
1126:
1125:
1123:
1122:
1117:
1112:
1107:
1102:
1097:
1091:
1089:
1085:
1084:
1081:
1080:
1078:
1077:
1072:
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1026:
1024:
1018:
1017:
1015:
1014:
1009:
1004:
999:
994:
989:
984:
974:
969:
964:
954:
949:
944:
939:
934:
929:
923:
921:
915:
914:
912:
911:
906:
901:
900:
899:
889:
884:
883:
882:
872:
867:
862:
857:
856:
855:
845:
840:
839:
838:
828:
823:
817:
815:
811:
810:
808:
807:
802:
797:
792:
791:
790:
780:
775:
770:
764:
762:
755:
749:
748:
746:
745:
740:
730:
725:
711:
706:
701:
696:
691:
689:Parallelizable
686:
681:
676:
675:
674:
664:
659:
654:
649:
644:
639:
634:
629:
624:
619:
609:
599:
593:
591:
585:
584:
582:
581:
576:
571:
569:Lie derivative
566:
564:Integral curve
561:
556:
551:
550:
549:
539:
534:
533:
532:
525:Diffeomorphism
522:
516:
514:
508:
507:
505:
504:
499:
494:
489:
484:
479:
474:
469:
464:
458:
456:
447:
446:
444:
443:
438:
433:
428:
423:
418:
413:
408:
403:
402:
401:
396:
386:
385:
384:
373:
371:
370:Basic concepts
367:
366:
356:
354:
353:
346:
339:
331:
323:
322:
305:
266:(2000-01-01).
254:
237:
180:
179:
177:
174:
173:
172:
167:
162:
157:
152:
147:
140:
137:
81:
80:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1288:
1277:
1274:
1272:
1269:
1268:
1266:
1255:
1250:
1248:
1243:
1241:
1236:
1235:
1229:
1227:
1223:
1219:
1214:
1211:
1207:
1194:
1191:
1189:
1188:Supermanifold
1186:
1184:
1181:
1179:
1176:
1172:
1169:
1168:
1167:
1164:
1162:
1159:
1157:
1154:
1152:
1149:
1147:
1144:
1142:
1139:
1137:
1134:
1133:
1131:
1127:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1092:
1090:
1086:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1027:
1025:
1023:
1019:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
979:
975:
973:
970:
968:
965:
963:
959:
955:
953:
950:
948:
945:
943:
940:
938:
935:
933:
930:
928:
925:
924:
922:
920:
916:
910:
909:Wedge product
907:
905:
902:
898:
895:
894:
893:
890:
888:
885:
881:
878:
877:
876:
873:
871:
868:
866:
863:
861:
858:
854:
853:Vector-valued
851:
850:
849:
846:
844:
841:
837:
834:
833:
832:
829:
827:
824:
822:
819:
818:
816:
812:
806:
803:
801:
798:
796:
793:
789:
786:
785:
784:
783:Tangent space
781:
779:
776:
774:
771:
769:
766:
765:
763:
759:
756:
754:
750:
744:
741:
739:
735:
731:
729:
726:
724:
720:
716:
712:
710:
707:
705:
702:
700:
697:
695:
692:
690:
687:
685:
682:
680:
677:
673:
670:
669:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
614:
610:
608:
604:
600:
598:
595:
594:
592:
586:
580:
577:
575:
572:
570:
567:
565:
562:
560:
557:
555:
552:
548:
547:in Lie theory
545:
544:
543:
540:
538:
535:
531:
528:
527:
526:
523:
521:
518:
517:
515:
513:
509:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
463:
460:
459:
457:
454:
450:Main results
448:
442:
439:
437:
434:
432:
431:Tangent space
429:
427:
424:
422:
419:
417:
414:
412:
409:
407:
404:
400:
397:
395:
392:
391:
390:
387:
383:
380:
379:
378:
375:
374:
372:
368:
363:
359:
352:
347:
345:
340:
338:
333:
332:
329:
315:
309:
306:
301:
297:
293:
289:
285:
281:
277:
273:
272:Acta Numerica
269:
265:
258:
255:
247:
241:
238:
233:
229:
225:
221:
217:
213:
208:
203:
199:
195:
191:
185:
182:
175:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
146:
143:
142:
138:
136:
134:
131:
127:
123:
119:
115:
111:
107:
103:
99:
95:
92:
88:
77:
74:
66:
56:
52:
46:
43:This article
41:
32:
31:
19:
1226:expanding it
1215:
1115:Moving frame
1110:Morse theory
1100:Gauge theory
892:Tensor field
821:Closed/Exact
800:Vector field
768:Distribution
709:Hypercomplex
704:Quaternionic
441:Vector field
399:Smooth atlas
308:
275:
271:
257:
240:
197:
193:
184:
130:nonholonomic
86:
84:
69:
60:
49:Please help
44:
1060:Levi-Civita
1050:Generalized
1022:Connections
972:Lie algebra
904:Volume form
805:Vector flow
778:Pushforward
773:Lie bracket
672:Lie algebra
637:G-structure
426:Pushforward
406:Submanifold
278:: 215–365.
133:constraints
1265:Categories
1183:Stratifold
1141:Diffeology
937:Associated
738:Symplectic
723:Riemannian
652:Hyperbolic
579:Submersion
487:Hopf–Rinow
421:Submersion
416:Smooth map
176:References
63:March 2017
1065:Principal
1040:Ehresmann
997:Subbundle
987:Principal
962:Fibration
942:Cotangent
814:Covectors
667:Lie group
647:Hermitian
590:manifolds
559:Immersion
554:Foliation
492:Noether's
477:Frobenius
472:De Rham's
467:Darboux's
358:Manifolds
300:121539932
292:1474-0508
207:1207.0069
150:Lie group
110:animation
1161:Orbifold
1156:K-theory
1146:Diffiety
870:Pullback
684:Oriented
662:Kenmotsu
642:Hadamard
588:Types of
537:Geodesic
362:Glossary
232:28406272
139:See also
114:vehicles
106:manifold
1105:History
1088:Related
1002:Tangent
980:)
960:)
927:Adjoint
919:Bundles
897:density
795:Torsion
761:Vectors
753:Tensors
736:)
721:)
717:,
715:Pseudo−
694:Poisson
627:Finsler
622:Fibered
617:Contact
615:)
607:Complex
605:)
574:Section
212:Bibcode
1070:Vector
1055:Koszul
1035:Cartan
1030:Affine
1012:Vector
1007:Tensor
992:Spinor
982:Normal
978:Stable
932:Affine
836:bundle
788:bundle
734:Almost
657:Kähler
613:Almost
603:Almost
597:Closed
497:Sard's
453:(list)
298:
290:
230:
94:method
1216:This
1178:Sheaf
952:Fiber
728:Rizza
699:Prime
530:Local
520:Curve
382:Atlas
317:(PDF)
296:S2CID
249:(PDF)
228:S2CID
202:arXiv
104:on a
89:is a
1222:stub
1045:Form
947:Dual
880:flow
743:Tame
719:Sub−
632:Flat
512:Maps
288:ISSN
120:and
96:for
967:Jet
280:doi
220:doi
198:257
116:in
53:by
1267::
958:Co
294:.
286:.
274:.
270:.
226:.
218:.
210:.
196:.
135:.
85:A
1253:e
1246:t
1239:v
1228:.
976:(
956:(
732:(
713:(
611:(
601:(
364:)
360:(
350:e
343:t
336:v
319:.
302:.
282::
276:9
251:.
234:.
222::
214::
204::
124:/
76:)
70:(
65:)
61:(
57:.
47:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.