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Volumn 63, Issue 2, 2009, Pages 225-249

Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations

Author keywords

control system; Hamiltonian; inverse problem; nonholonomic system; Pontryagin's principle; quantization

Indexed keywords


EID: 67649158632     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(09)90001-5     Document Type: Article
Times cited : (28)

References (27)
  • 2
    • 0001765490 scopus 로고
    • The inverse problem of the calculus of variations for ordinary differential equations
    • Anderson I.M., and Thompson G. The inverse problem of the calculus of variations for ordinary differential equations. Mem. Amer. Math. Soc. 98 no. 473 (1992)
    • (1992) Mem. Amer. Math. Soc. , vol.98 , Issue.473
    • Anderson, I.M.1    Thompson, G.2
  • 3
    • 0346241309 scopus 로고    scopus 로고
    • collaboration of J. Baillieul, P. Crouch and J.E. Marsden, Springer, NY
    • Bloch A.M., collaboration of J. Baillieul, and P. Crouch and J.E. Marsden. Nonholonomic Mechanics and Control (2003), Springer, NY
    • (2003) Nonholonomic Mechanics and Control
    • Bloch, A.M.1
  • 4
    • 47949091665 scopus 로고    scopus 로고
    • Quantization of a nonholonomic system
    • Bloch A.M., and Rojo A. Quantization of a nonholonomic system. Phys. Rev. Letters 101 (2008) 030404
    • (2008) Phys. Rev. Letters , vol.101 , pp. 030404
    • Bloch, A.M.1    Rojo, A.2
  • 6
    • 0001276535 scopus 로고
    • Rigidity of integral curves of rank 2 distributions
    • Bryant R.L., and Hsu L. Rigidity of integral curves of rank 2 distributions. Invent. Math. 114 (1993) 435-461
    • (1993) Invent. Math. , vol.114 , pp. 435-461
    • Bryant, R.L.1    Hsu, L.2
  • 9
    • 0035645521 scopus 로고    scopus 로고
    • Nonholonomic integrators
    • Cortes J., and Martinez S. Nonholonomic integrators. Nonlinearity 14 (2001) 1365-1392
    • (2001) Nonlinearity , vol.14 , pp. 1365-1392
    • Cortes, J.1    Martinez, S.2
  • 10
    • 48949092128 scopus 로고    scopus 로고
    • The inverse problem for invariant Lagrangians on a Lie group
    • Crampin M., and Mestdag T. The inverse problem for invariant Lagrangians on a Lie group. J. Lie Theory 18 (2008) 471-502
    • (2008) J. Lie Theory , vol.18 , pp. 471-502
    • Crampin, M.1    Mestdag, T.2
  • 11
    • 0001272670 scopus 로고
    • Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations
    • Crampin M., Sarlet W., Bymes G.B., and Prince G.E. Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations. Inverse Problems 10 (1994) 245-260
    • (1994) Inverse Problems , vol.10 , pp. 245-260
    • Crampin, M.1    Sarlet, W.2    Bymes, G.B.3    Prince, G.E.4
  • 12
    • 84942830232 scopus 로고
    • Solution of the inverse problem of the calculus of variations
    • Douglas J. Solution of the inverse problem of the calculus of variations. Trans. Amer. Math. Soc. 50 (1941) 71-128
    • (1941) Trans. Amer. Math. Soc. , vol.50 , pp. 71-128
    • Douglas, J.1
  • 13
    • 0000610857 scopus 로고
    • The quantum mechanics of non-holonomic systems
    • Eden R.J. The quantum mechanics of non-holonomic systems. Proc. Royal Soc. London 205 (1951) 583-595
    • (1951) Proc. Royal Soc. London , vol.205 , pp. 583-595
    • Eden, R.J.1
  • 14
    • 85014806128 scopus 로고    scopus 로고
    • Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization
    • Progr. Math. 232, Boston
    • Ehlers K., Koiller J., Montgomery R., and Rios P.M. Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization. The breadth of symplectic and Poisson geometry (2005), Progr. Math. 232, Boston 75-120
    • (2005) The breadth of symplectic and Poisson geometry , pp. 75-120
    • Ehlers, K.1    Koiller, J.2    Montgomery, R.3    Rios, P.M.4
  • 15
    • 23444455474 scopus 로고    scopus 로고
    • Discrete Nonholonomic LL systems on Lie Groups
    • Fedorov Y.N., and Zenkov V. Discrete Nonholonomic LL systems on Lie Groups. Nonlinearity 18 (2005) 2211-2241
    • (2005) Nonlinearity , vol.18 , pp. 2211-2241
    • Fedorov, Y.N.1    Zenkov, V.2
  • 16
    • 52349084338 scopus 로고    scopus 로고
    • O. E. Fernandez and A. M. Bloch: Equivalence of the Dynamics of Nonholonomic and Variational Nonholonomic Systems for certain Initial Data, J. Phys. A: Math. Theor.41 344005 (20 pp).
    • O. E. Fernandez and A. M. Bloch: Equivalence of the Dynamics of Nonholonomic and Variational Nonholonomic Systems for certain Initial Data, J. Phys. A: Math. Theor.41 344005 (20 pp).
  • 22
    • 0001707439 scopus 로고
    • Variational principles for constrained systems: theory and experiment
    • Lewis A., and Murray R. Variational principles for constrained systems: theory and experiment. The Intl. J. Nonlinear Mechanics 30 (1995) 793-815
    • (1995) The Intl. J. Nonlinear Mechanics , vol.30 , pp. 793-815
    • Lewis, A.1    Murray, R.2
  • 23
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • Marsden J.E., and West M. Discrete mechanics and variational integrators. Acta Numer. 10 (2001) 357-514
    • (2001) Acta Numer. , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 25
    • 51649141673 scopus 로고
    • Quantization of a non-holonomic system with symmetry
    • Pitanga P. Quantization of a non-holonomic system with symmetry. Il Nuovo Cimento B 109 (1994) 583-594
    • (1994) Il Nuovo Cimento B , vol.109 , pp. 583-594
    • Pitanga, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.