메뉴 건너뛰기




Volumn 19, Issue 6, 2006, Pages 1313-1348

Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33646736110     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/19/6/006     Document Type: Article
Times cited : (67)

References (29)
  • 1
    • 0007133485 scopus 로고    scopus 로고
    • Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
    • 10.1023/A:1007654605901 0377-9017
    • Bobenko A I and Suris Y B 1999 Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products Lett. Math. Phys. 49 79-93
    • (1999) Lett. Math. Phys. , vol.49 , Issue.1 , pp. 79-93
    • Bobenko, A.I.1    Suris, Y.B.2
  • 2
    • 0033247267 scopus 로고    scopus 로고
    • Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
    • 10.1007/s002200050642 0010-3616
    • Bobenko A I and Suris Y B 1999 Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top Commun. Math. Phys. 204 147-88
    • (1999) Commun. Math. Phys. , vol.204 , Issue.1 , pp. 147-188
    • Bobenko, A.I.1    Suris, Y.B.2
  • 8
    • 0000855801 scopus 로고
    • Algebraic constructions in the category of Lie algebroids
    • 10.1016/0021-8693(90)90246-K 0021-8693
    • Higgins P J and Mackenzie K 1990 Algebraic constructions in the category of Lie algebroids J. Algebra 129 194-230
    • (1990) J. Algebra , vol.129 , Issue.1 , pp. 194-230
    • Higgins, P.J.1    MacKenzie, K.2
  • 10
    • 0002761713 scopus 로고
    • Espaces variationnels et mécanique
    • 0373-0956
    • Klein J 1962 Espaces variationnels et mécanique Ann. Inst. Fourier 12 1-124
    • (1962) Ann. Inst. Fourier , vol.12 , pp. 1-124
    • Klein, J.1
  • 11
    • 33646227988 scopus 로고    scopus 로고
    • Leok M 2004 Foundations of computational geometric mechanics, control and dynamical systems Thesis California Institute of Technology available at http://www.math.lsa.umich.edu/mleok
    • (2004) Thesis
    • Leok, M.1
  • 13
    • 19844361844 scopus 로고    scopus 로고
    • Lagrangian submanifolds and dynamics on Lie algebroids
    • 0305-4470 R01
    • de Len M, Marrero J C and Martínez E 2005 Lagrangian submanifolds and dynamics on Lie algebroids J. Phys. A: Math. Gen. 38 R241-308
    • (2005) J. Phys. A: Math. Gen. , vol.38 , Issue.24
    • De Len, M.1    Marrero, J.C.2    Martínez, E.3
  • 14
    • 33646721235 scopus 로고    scopus 로고
    • Reduction of simple mechanical systems
    • Lewis A 1997 Reduction of simple mechanical systems Mechanics and Symmetry Seminars (University of Warwick) http://penelope.mast.queensu.ca/ andrew/
    • (1997) Mechanics and Symmetry Seminars
    • Lewis, A.1
  • 15
    • 0010105520 scopus 로고
    • Sur les groupoides différentiables et le 'presque parallélisme'
    • 0082-0725
    • Libermann P 1972 Sur les groupoides différentiables et le 'presque parallélisme' Symp. Math. 10 59-93
    • (1972) Symp. Math. , vol.10 , pp. 59-93
    • Libermann, P.1
  • 17
    • 0000636313 scopus 로고
    • Double Lie algebroids and second order geometry
    • 10.1016/0001-8708(92)90036-K 0001-8708
    • Mackenzie K 1992 Double Lie algebroids and second order geometry Adv. Math. 94 180-239
    • (1992) Adv. Math. , vol.94 , Issue.2 , pp. 180-239
    • MacKenzie, K.1
  • 18
    • 0033228880 scopus 로고    scopus 로고
    • Discrete Euler-Poincaré and Lie-Poisson equations
    • 0951-7715 314
    • Marsden J E, Pekarsky S and Shkoller S 1999 Discrete Euler- Poincaré and Lie-Poisson equations Nonlinearity 12 1647-62
    • (1999) Nonlinearity , vol.12 , Issue.6 , pp. 1647-1662
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3
  • 19
    • 0007071020 scopus 로고    scopus 로고
    • Symmetry reduction of discrete Lagrangian mechanics on Lie groups
    • 10.1016/S0393-0440(00)00018-8 0393-0440
    • Marsden J E, Pekarsky S and Shkoller S 1999 Symmetry reduction of discrete Lagrangian mechanics on Lie groups J. Geom. Phys. 36 140-51
    • (1999) J. Geom. Phys. , vol.36 , Issue.1-2 , pp. 140-151
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3
  • 20
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • 10.1017/S096249290100006X 0962-4929
    • Marsden J E and West M 2001 Discrete mechanics and variational integrators Acta Numer. 10 357-514
    • (2001) Acta Numer. , vol.10 , Issue.0 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 21
    • 0035385190 scopus 로고    scopus 로고
    • Lagrangian mechanics on Lie algebroids
    • 10.1023/A:1011965919259 0167-8019
    • Martínez E 2001 Lagrangian mechanics on Lie algebroids Acta Appl. Math. 67 295-320
    • (2001) Acta Appl. Math. , vol.67 , Issue.3 , pp. 295-320
    • Martínez, E.1
  • 22
    • 8644261436 scopus 로고    scopus 로고
    • Geometric formulation of mechanics on Lie algebroids
    • Martínez E 2001 Geometric formulation of mechanics on Lie algebroids Proc. 8th Fall Workshop on Geometry and Physics (Medina del Campo, 1999) Publ. de la RSME 2 209-22
    • (2001) Publ. de la RSME , vol.2 , pp. 209-222
    • Martínez, E.1
  • 23
    • 0031492543 scopus 로고    scopus 로고
    • Matched pair of Lie algebroids
    • Mokri T 1997 Matched pair of Lie algebroids Glasgow Math. J. 39 167-81
    • (1997) Glasgow Math. J. , vol.39 , pp. 167-181
    • Mokri, T.1
  • 24
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • 10.1007/BF02352494 0010-3616
    • Moser J and Veselov A P 1991 Discrete versions of some classical integrable systems and factorization of matrix polynomials Commun. Math. Phys. 139 217-43
    • (1991) Commun. Math. Phys. , vol.139 , Issue.2 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 25
    • 33646751352 scopus 로고
    • Ostrowski J P 1995 The mechanics and control of undulatory robotic locomotion PhD Thesis California Institute of Technology
    • (1995) PhD Thesis
    • Ostrowski, J.P.1
  • 26
    • 0010696742 scopus 로고    scopus 로고
    • Geometric objects defined by almost Lie structures
    • Popescu M and Popescu P 2001 Geometric objects defined by almost Lie structures Proc. Workshop on Lie Algebroids and Related Topics in Differential Geometry (Warsaw 2001) Banach Center Publ. 54 217-33
    • (2001) Banach Center Publ. , vol.54 , pp. 217-233
    • Popescu, M.1    Popescu, P.2
  • 28
    • 4644257092 scopus 로고    scopus 로고
    • Prolongations of Lie groupoids and Lie algebroids
    • Saunders D 2004 Prolongations of Lie groupoids and Lie algebroids Houston J. Math. 30 637-55
    • (2004) Houston J. Math. , vol.30 , pp. 637-655
    • Saunders, D.1
  • 29
    • 0000714030 scopus 로고    scopus 로고
    • Lagrangian mechanics and groupoids
    • 1069-5265
    • Weinstein A 1996 Lagrangian mechanics and groupoids Fields Inst. Commun. 7 207-31
    • (1996) Fields Inst. Commun. , vol.7 , pp. 207-231
    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.