메뉴 건너뛰기




Volumn 19, Issue 3, 2007, Pages 235-253

Higher order geodesics in Lie groups

Author keywords

Geodesic; Lax equation; Lie group; Lie quadratic; Riemannian cubic; Riemannian polynomial

Indexed keywords

CONSTANT OF MOTION; DUALITY THEORY; EULER-LAGRANGE EQUATIONS; HIGHER ORDER; LAX EQUATION; LAX PAIRS; LIE ALGEBRA; LIE GROUP; LIE QUADRATICS; RIEMANNIAN CUBICS; RIEMANNIAN MANIFOLD; RIEMANNIAN METRICS; RIGID-BODY MOTION; ROTATION GROUP; SECOND ORDERS;

EID: 74849089706     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-007-0012-x     Document Type: Article
Times cited : (23)

References (36)
  • 3
    • 0036226982 scopus 로고    scopus 로고
    • Euclidean metrics for motion generation on SE(3)
    • C Belta V Kumar 2002 Euclidean metrics for motion generation on SE(3) J Mech Eng Sci C 216 47 60
    • (2002) J Mech Eng Sci C , vol.216 , pp. 47-60
    • Belta, C.1    Kumar, V.2
  • 6
    • 0001480429 scopus 로고    scopus 로고
    • On the geometry of Riemannian cubic polynomials
    • DOI 10.1016/S0926-2245(01)00054-7, PII S0926224501000547
    • M Camarinha F Silva Leite P Crouch 2001 On the geometry of Riemannian cubic polynomials Diff Geom Appl 15 107 135 1034.53041 10.1016/S0926-2245(01) 00054-7 1857558 (Pubitemid 33654692)
    • (2001) Differential Geometry and its Application , vol.15 , Issue.2 , pp. 107-135
    • Camarinha, M.1    Silva Leite, F.2    Crouch, P.3
  • 7
    • 0033155646 scopus 로고    scopus 로고
    • De Casteljau algorithm on Lie groups and spheres
    • DOI 10.1023/A:1021770717822
    • P Crouch G Kun F Silva Leite 1999 The de Casteljau algorithm on Lie groups and spheres J Dyn Control Syst 5 397 429 0961.53027 10.1023/A: 1021770717822 1706785 (Pubitemid 32080737)
    • (1999) Journal of Dynamical and Control Systems , vol.5 , Issue.3 , pp. 397-429
    • Crouch, P.1    Kun, G.2    Silva Leite, F.3
  • 8
    • 0026400341 scopus 로고
    • Geometry and the dynamic interpolation problem
    • Boston
    • Crouch P, Silva Leite F (1991) Geometry and the dynamic interpolation problem. Proc Amer Control Conf, Boston, pp 1131-1136
    • (1991) Proc Amer Control Conf , pp. 1131-1136
    • Crouch, P.1    Silva Leite, F.2
  • 9
    • 0001261818 scopus 로고
    • The dynamic interpolation problem: On Riemannian manifolds, Lie groups and symmetric spaces
    • 0946.58018 10.1007/BF02254638 1333770
    • P Crouch F Silva Leite 1995 The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces J Dyn Control Syst 1 177 202 0946.58018 10.1007/BF02254638 1333770
    • (1995) J Dyn Control Syst , vol.1 , pp. 177-202
    • Crouch, P.1    Silva Leite, F.2
  • 12
    • 0028499355 scopus 로고
    • Geometric construction of Bézier motions
    • 10.1115/1.2919446
    • Q Ge B Ravani 1994 Geometric construction of Bézier motions Trans ASME J Mech Des 116 749 755 10.1115/1.2919446
    • (1994) Trans ASME J Mech des , vol.116 , pp. 749-755
    • Ge, Q.1    Ravani, B.2
  • 13
    • 0036913308 scopus 로고    scopus 로고
    • An analytical theory for Riemannian cubic polynomials
    • 1138.58307 10.1093/imamci/19.4.445 1949013
    • R Giambo F Giannoni P Piccione 2002 An analytical theory for Riemannian cubic polynomials IMA J Math Control Inform 19 445 460 1138.58307 10.1093/imamci/19.4.445 1949013
    • (2002) IMA J Math Control Inform , vol.19 , pp. 445-460
    • Giambo, R.1    Giannoni, F.2    Piccione, P.3
  • 14
    • 2342593307 scopus 로고    scopus 로고
    • Optimal control on Riemannian manifolds by interpolation
    • 1082.58016 10.1007/s00498-003-0139-3 2052377
    • R Giambo F Giannoni P Piccione 2004 Optimal control on Riemannian manifolds by interpolation Math Control Signals Syst 16 278 296 1082.58016 10.1007/s00498-003-0139-3 2052377
    • (2004) Math Control Signals Syst , vol.16 , pp. 278-296
    • Giambo, R.1    Giannoni, F.2    Piccione, P.3
  • 15
    • 8744268680 scopus 로고    scopus 로고
    • Dynamic interpolation on Riemannian manifolds: An application to interferometric imaging
    • Boston
    • Hussein I, Bloch A (2004) Dynamic interpolation on Riemannian manifolds: an application to interferometric imaging. Proc Amer Control Conf, Boston, pp 413-418
    • (2004) Proc Amer Control Conf , pp. 413-418
    • Hussein, I.1    Bloch, A.2
  • 16
    • 0004293970 scopus 로고
    • Interscience New York 0121.27504
    • Jacobson N (1962) Lie algebras. Interscience, New York
    • (1962) Lie Algebras
    • Jacobson, N.1
  • 19
    • 20844437032 scopus 로고    scopus 로고
    • Envelopes of splines in the projective plane
    • DOI 10.1093/imamci/dni014
    • K Krakowski 2005 Envelopes of splines in the projective plane IMA J Math Control Inform 22 171 180 1095.41009 10.1093/imamci/dni014 2141922 (Pubitemid 40858206)
    • (2005) IMA Journal of Mathematical Control and Information , vol.22 , Issue.2 , pp. 171-180
    • Krakowski, K.A.1
  • 20
    • 0004190360 scopus 로고
    • Princeton University Press Princeton 0108.10401
    • Milnor J (1963) Morse theory. Princeton University Press, Princeton
    • (1963) Morse Theory
    • Milnor, J.1
  • 21
    • 0037363153 scopus 로고    scopus 로고
    • Null cubics and Lie quadratics
    • DOI 10.1063/1.1537461
    • L Noakes 2003 Null cubics and Lie quadratics J Math Phys 44 1436 1448 1062.53007 10.1063/1.1537461 1958275 (Pubitemid 36446145)
    • (2003) Journal of Mathematical Physics , vol.44 , Issue.3 , pp. 1436-1448
    • Noakes, L.1
  • 23
    • 33745662909 scopus 로고    scopus 로고
    • Duality and Riemannian cubics
    • DOI 10.1007/s10444-004-7621-4
    • L Noakes 2006 Duality and Riemannian cubics Adv Comput Math 25 195 209 1096.53008 10.1007/s10444-004-7621-4 2231701 (Pubitemid 43974374)
    • (2006) Advances in Computational Mathematics , vol.25 , Issue.1-3 , pp. 195-209
    • Noakes, L.1
  • 24
    • 33845433433 scopus 로고    scopus 로고
    • Lax constraints in semisimple lie groups
    • DOI 10.1093/qmath/hal002
    • L Noakes 2006 Lax constraints in semisimple Lie groups Q J Math 57 527 538 10.1093/qmath/hal002 05302351 2277599 (Pubitemid 44906069)
    • (2006) Quarterly Journal of Mathematics , vol.57 , Issue.4 , pp. 527-538
    • Noakes, L.1
  • 25
    • 0024929710 scopus 로고
    • Cubic splines on curved spaces
    • 0698.58018 10.1093/imamci/6.4.465 1036158
    • L Noakes G Heinzinger B Paden 1989 Cubic splines on curved spaces IMA J Math Control Inform 6 465 473 0698.58018 10.1093/imamci/6.4.465 1036158
    • (1989) IMA J Math Control Inform , vol.6 , pp. 465-473
    • Noakes, L.1    Heinzinger, G.2    Paden, B.3
  • 26
    • 33845419214 scopus 로고    scopus 로고
    • Quadratures and cubics in SO(3) and SO(1,2)
    • 10.1093/imamci/dni069 2271173
    • L Noakes T Popiel 2005 Quadratures and cubics in SO(3) and SO(1,2) IMA J Math Control Inform 23 463 473 10.1093/imamci/dni069 2271173
    • (2005) IMA J Math Control Inform , vol.23 , pp. 463-473
    • Noakes, L.1    Popiel, T.2
  • 27
    • 0029277611 scopus 로고
    • Bézier curves on Riemannian manifolds and Lie groups with kinematic applications
    • F Park B Ravani 1995 Bézier curves on Riemannian manifolds and Lie groups with kinematic applications Trans ASME J Mech Des 117 36 40
    • (1995) Trans ASME J Mech des , vol.117 , pp. 36-40
    • Park, F.1    Ravani, B.2
  • 28
    • 0031189315 scopus 로고    scopus 로고
    • Smooth invariant interpolation of rotations
    • 10.1145/256157.256160
    • F Park B Ravani 1997 Smooth invariant interpolation of rotations ACM Trans Graph 16 277 295 10.1145/256157.256160
    • (1997) ACM Trans Graph , vol.16 , pp. 277-295
    • Park, F.1    Ravani, B.2
  • 29
    • 33344466154 scopus 로고    scopus 로고
    • 2 spherical Bézier splines
    • DOI 10.1016/j.cagd.2005.11.003, PII S0167839605001469
    • 2 spherical Bézier splines Comput Aided Geom Des 23 261 275 1094.65014 10.1016/j.cagd.2005.11.003 2207631 (Pubitemid 43288846)
    • (2006) Computer Aided Geometric Design , vol.23 , Issue.3 , pp. 261-275
    • Popiel, T.1    Noakes, L.2
  • 30
    • 0022095776 scopus 로고
    • Animating rotations with quaternion curves
    • 10.1145/325165.325242
    • K Shoemake 1985 Animating rotations with quaternion curves ACM SIGGRAPH Comput Graph 19 245 254 10.1145/325165.325242
    • (1985) ACM SIGGRAPH Comput Graph , vol.19 , pp. 245-254
    • Shoemake, K.1
  • 32
    • 0033687223 scopus 로고    scopus 로고
    • Elastic curves as solutions of sub-Riemannian control problems
    • 1048.58010 10.1007/PL00009863 1771656
    • F Silva Leite M Camarinha P Crouch 2000 Elastic curves as solutions of sub-Riemannian control problems Math Control Signals Syst 13 140 155 1048.58010 10.1007/PL00009863 1771656
    • (2000) Math Control Signals Syst , vol.13 , pp. 140-155
    • Silva Leite, F.1    Camarinha, M.2    Crouch, P.3
  • 34
    • 0000453725 scopus 로고    scopus 로고
    • Interpolation schemes for rigid body motions
    • 10.1016/S0010-4485(97)00060-2 0904.68179
    • M Žefran V Kumar 1998 Interpolation schemes for rigid body motions Comput Aided Des 30 179 189 10.1016/S0010-4485(97)00060-2 0904.68179
    • (1998) Comput Aided des , vol.30 , pp. 179-189
    • Žefran, M.1    Kumar, V.2
  • 36
    • 0032138442 scopus 로고    scopus 로고
    • On the generation of smooth three-dimensional rigid body motions
    • 10.1109/70.704225
    • M Žefran V Kumar C Croke 1998 On the generation of smooth three-dimensional rigid body motions IEEE Trans Robot Autom 14 576 589 10.1109/70.704225
    • (1998) IEEE Trans Robot Autom , vol.14 , pp. 576-589
    • Žefran, M.1    Kumar, V.2    Croke, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.