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Volumn 46, Issue 3-4, 2003, Pages 203-230

A connection theoretic approach to sub-Riemannian geometry

Author keywords

Connections; Nonholonomic mechanics; Sub Riemannian geometry; Vakonomic dynamics

Indexed keywords


EID: 0037410296     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(02)00026-8     Document Type: Article
Times cited : (14)

References (20)
  • 1
    • 0032206308 scopus 로고    scopus 로고
    • Newton's law and integrability of nonholonomic systems
    • Bloch A.M.Crouch P.E.Newton's law and integrability of nonholonomic systems SIAM J. Contr. Optim. 36 1998 2020-2039
    • (1998) SIAM J. Contr. Optim. , vol.36 , pp. 2020-2039
    • Bloch, A.M.1    Crouch, P.E.2
  • 2
    • 0004250608 scopus 로고
    • Differentiable Manifolds: An Introduction
    • Van Nostrand Reinhold, London
    • F. Brickell, R.S. Clark, Differentiable Manifolds: An Introduction, Van Nostrand Reinhold, London, 1970.
    • (1970)
    • Brickell, F.1    Clark, R.S.2
  • 4
    • 0037404265 scopus 로고    scopus 로고
    • Generalised connections over a vector bundle map
    • in press
    • F. Cantrijn, B. Langerock, Generalised connections over a vector bundle map, Diff. Geom. Appl. (2003), in press.
    • (2003) Diff. Geom. Appl.
    • Cantrijn, F.1    Langerock, B.2
  • 6
    • 34250951325 scopus 로고
    • Über systeme von linearen partiellen differentialgleichungen erseter
    • Chow W.L.Über systeme von linearen partiellen differentialgleichungen erseter ordnung Math. Ann. 117 1939 98 105
    • (1939) Math. Ann. , vol.117 , pp. 98-105
    • Chow, W.L.1
  • 7
    • 0013302384 scopus 로고    scopus 로고
    • Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions
    • J. Cortés, M. de Léon, D. Mart́n de Diego, S. Mart́nez, Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions, SIAM J. Control Optim. 41 (5) (2003) 1389-1412.
    • (2003) SIAM J. Control Optim. , vol.41 , Issue.5 , pp. 1389-1412
    • Cortés, J.1    de Léon, M.2    Mart́n de Diego, D.3    Mart́nez, S.4
  • 8
    • 0000470538 scopus 로고    scopus 로고
    • Connections in Poisson geometry. I. Holonomy and invariants
    • R.L. Fernandes, Connections in Poisson geometry. I. Holonomy and invariants, J. Diff. Geom. 54 (2) (2000) 303-365.
    • (2000) J. Diff. Geom. , vol.54 , Issue.2 , pp. 303-365
    • Fernandes, R.L.1
  • 9
    • 0036748231 scopus 로고    scopus 로고
    • Lie Algebroids, Holonomy and Characteristic Classes
    • R.L. Fernandes, Lie Algebroids, Holonomy and Characteristic Classes, Adv. Math. 170 (1) (2002) 119-179.
    • (2002) Adv. Math. , vol.170 , Issue.1 , pp. 119-179
    • Fernandes, R.L.1
  • 12
    • 0035834620 scopus 로고    scopus 로고
    • Nonholonomic mechanics and connections over a bundle map
    • B. Langerock, Nonholonomic mechanics and connections over a bundle map, J. Phys. A 34 (2001) L609-L615.
    • (2001) J. Phys. A , vol.34
    • Langerock, B.1
  • 14
    • 0003241549 scopus 로고
    • Shortest paths for sub Riemannian metrics on rank two distributions
    • W. Liu, H.J. Sussmann, Shortest paths for sub Riemannian metrics on rank two distributions, Memoirs AMS 118 (1995).
    • (1995) Memoirs AMS , vol.118
    • Liu, W.1    Sussmann, H.J.2
  • 16
    • 0001753741 scopus 로고    scopus 로고
    • Variational aspects of the geodesics problem in sub-Riemannian geometry
    • Piccione P.Tausk D.V.Variational aspects of the geodesics problem in sub-Riemannian geometry J. Geom. Phys. 39 2001 183-206
    • (2001) J. Geom. Phys. , vol.39 , pp. 183-206
    • Piccione, P.1    Tausk, D.V.2
  • 18
    • 84972551517 scopus 로고
    • Sub-Riemannian geometry
    • Strichartz R.S.Sub-Riemannian geometry J. Diff. Geom. 24 1986 221-263
    • (1986) J. Diff. Geom. , vol.24 , pp. 221-263
    • Strichartz, R.S.1
  • 19
    • 84972492827 scopus 로고
    • Corrections to sub-Riemannian geometry
    • Strichartz R.S.Corrections to sub-Riemannian geometry J. Diff. Geom. 30 1989 595-596
    • (1989) J. Diff. Geom. , vol.30 , pp. 595-596
    • Strichartz, R.S.1
  • 20
    • 0001590046 scopus 로고    scopus 로고
    • An introduction to the coordinate-free maximum principle
    • B. Jakubcyzk, W. Respondek (Eds.), Marcel Dekker, New York
    • H.J. Sussmann, An introduction to the coordinate-free maximum principle, in: B. Jakubcyzk, W. Respondek (Eds.), Geometry of Feedback and Optimal Control, Marcel Dekker, New York, 1997, pp. 463-557.
    • (1997) Geometry of Feedback and Optimal Control , pp. 463-557
    • Sussmann, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.