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Volumn 2, Issue 4, 2005, Pages 597-618

Geometric aspects of time-dependent singular differential equations

Author keywords

Constrained system; Implicit differential equation; Jet bundle; Singular lagrangian; Time dependent system; Vector hull

Indexed keywords


EID: 33746305568     PISSN: 02198878     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219887805000697     Document Type: Article
Times cited : (23)

References (31)
  • 2
    • 45849120114 scopus 로고
    • Torseurs sur un espace affine
    • in L. Schwartz (Hermann, Paris)
    • Y. Bamberger et J.-P. Bourguignon, Torseurs sur un espace affine, in Les tenseurs, L. Schwartz (Hermann, Paris, 1975), pp. 151-202.
    • (1975) Les Tenseurs , pp. 151-202
    • Bamberger, Y.1    Bourguignon, J.-P.2
  • 3
    • 0003259286 scopus 로고    scopus 로고
    • Numerical solution of initial-value problems in differential-algebraic equations
    • in (SIAM, Philadelphia)
    • K. E. Brenan, S. L. Campbell and L. R. Petzold, Numerical solution of initial-value problems in differential-algebraic equations, in Classics in Applied Mathematics 14, (SIAM, Philadelphia, 1996).
    • (1996) Classics in Applied Mathematics , vol.14
    • Brenan, K.E.1    Campbell, S.L.2    Petzold, L.R.3
  • 4
    • 0003649603 scopus 로고
    • (Springer-Verlag, Berlin) (translated from the original French edition of 1977)
    • M. Berger, Geometry I (Springer-Verlag, Berlin, 1987), (translated from the original French edition of 1977).
    • (1987) Geometry I
    • Berger, M.1
  • 5
    • 84990727291 scopus 로고
    • Theory of singular lagrangians
    • J. F. Cariñena, Theory of singular lagrangians, Fortschr. Phys. 38 (1990) 641-679.
    • (1990) Fortschr. Phys. , vol.38 , pp. 641-679
    • Cariñena, J.F.1
  • 6
    • 84990709853 scopus 로고
    • Geometric theory of time-dependent singular lagrangians
    • J. F. Cariñena and J. Fernández-Núñez, Geometric theory of time-dependent singular lagrangians, Fortschr. Phys. 41 (1993) 517-552.
    • (1993) Fortschr. Phys. , vol.41 , pp. 517-552
    • Cariñena, J.F.1    Fernández-Núñez, J.2
  • 7
    • 21344481635 scopus 로고
    • The constraint algorithm for time-dependent lagrangians
    • D. Chinea, M. de León and J. C. Marrero, The constraint algorithm for time-dependent lagrangians, J. Math. Phys. 35 (1994) 3410-3447.
    • (1994) J. Math. Phys. , vol.35 , pp. 3410-3447
    • Chinea, D.1    de León, M.2    Marrero, J.C.3
  • 8
    • 0037194396 scopus 로고    scopus 로고
    • Skinner-Rusk approach to time-dependent mechanics
    • J. Cortés, S. Martínez and F. Cantrijn, Skinner-Rusk approach to time-dependent mechanics, Phys. Lett. A300 (2002) 250-258.
    • (2002) Phys. Lett. , vol.A300 , pp. 250-258
    • Cortés, J.1    Martínez, S.2    Cantrijn, F.3
  • 10
    • 0001317137 scopus 로고
    • Geometrical setting of time-dependent regular systems. Alternative models
    • A. Echeverría Enríquez, M. C. Muñoz Lecanda and N. Román Roy, Geometrical setting of time-dependent regular systems. Alternative models, Rev. Math. Phys. 3 (1991) 301-330.
    • (1991) Rev. Math. Phys. , vol.3 , pp. 301-330
    • Echeverría, A.1    Enríquez2    Muñoz, M.C.3    Lecanda4    Román Roy, N.5
  • 11
    • 36749116497 scopus 로고
    • Presymplectic manifolds and the Dirac-Bergmann theory of constraints
    • M. J. Gotay J. M. Nester and G. Hinds, Presymplectic manifolds and the Dirac-Bergmann theory of constraints, J. Math. Phys. 19 (1978) 2388-2399.
    • (1978) J. Math. Phys. , vol.19 , pp. 2388-2399
    • Gotay, M.J.1    Nester, J.M.2    Hinds, G.3
  • 12
    • 13744259339 scopus 로고    scopus 로고
    • Regularity and symmetries of nonholonomic systems
    • X. Gràcia and R. Martín, Regularity and symmetries of nonholonomic systems, J. Phys. A: Math. Gen. 38 (2005) 1071-1087.
    • (2005) J. Phys. A: Math. Gen. , vol.38 , pp. 1071-1087
    • Gràcia, X.1    Martín, R.2
  • 13
    • 33746307078 scopus 로고    scopus 로고
    • Vector hulls of affine spaces and affine bundles
    • in preparation
    • X. Gràcia and R. Martín, Vector hulls of affine spaces and affine bundles, in preparation.
    • Gràcia, X.1    Martín, R.2
  • 15
    • 0039862111 scopus 로고
    • Constrained systems: A unified geometric approach
    • X. Gràcia and J. M. Pons, Constrained systems: A unified geometric approach, Int. J. Theor. Phys. 30 (1991) 511-516.
    • (1991) Int. J. Theor. Phys. , vol.30 , pp. 511-516
    • Gràcia, X.1    Pons, J.M.2
  • 16
    • 0001146699 scopus 로고
    • A generalized geometric framework for constrained systems
    • X. Gràcia and J. M. Pons, A generalized geometric framework for constrained systems, Diff. Geom. Appl. 2 (1992) 223-247.
    • (1992) Diff. Geom. Appl. , vol.2 , pp. 223-247
    • Gràcia, X.1    Pons, J.M.2
  • 17
    • 0041969799 scopus 로고    scopus 로고
    • Symmetries and infinitesimal symmetries of singular differential equations
    • X. Gràcia and J. M. Pons, Symmetries and infinitesimal symmetries of singular differential equations, J. Phys. A: Math. Gen. 35 (2002) 5059-5077.
    • (2002) J. Phys. A: Math. Gen. , vol.35 , pp. 5059-5077
    • Gràcia, X.1    Pons, J.M.2
  • 23
    • 0036837579 scopus 로고    scopus 로고
    • Lie algebroid structures and lagrangian systems on affine bundles
    • E. Martínez, T. Mestdag and W. Sarlet, Lie algebroid structures and lagrangian systems on affine bundles, J. Geom. Phys. 44 (2002) 70-95.
    • (2002) J. Geom. Phys. , vol.44 , pp. 70-95
    • Martínez, E.1    Mestdag, T.2    Sarlet, W.3
  • 24
    • 0344088385 scopus 로고    scopus 로고
    • Legendre transformation and analytical mechanics: A geometric approach
    • E. Massa, E. Pagani and S. Vignolo, Legendre transformation and analytical mechanics: A geometric approach, J. Math. Phys. 44 (2003) 1709-1722.
    • (2003) J. Math. Phys. , vol.44 , pp. 1709-1722
    • Massa, E.1    Pagani, E.2    Vignolo, S.3
  • 27
    • 0000877389 scopus 로고
    • A geometric treatment of implicit differential-algebraic equations
    • P. J. Rabier and W. C. Rheinboldt, A geometric treatment of implicit differential-algebraic equations, J. Differential Equations 109 (1994) 110-146.
    • (1994) J. Differential Equations , vol.109 , pp. 110-146
    • Rabier, P.J.1    Rheinboldt, W.C.2
  • 28
    • 0003209247 scopus 로고
    • The geometry of jet bundles
    • in (Cambridge University Press, Cambridge)
    • D. J. Saunders, The geometry of jet bundles, in London Mat. Soc. Lecture Note Series, Vol. 142 (Cambridge University Press, Cambridge, 1989).
    • (1989) London Mat. Soc. Lecture Note Series , vol.142
    • Saunders, D.J.1
  • 29
    • 36749105971 scopus 로고
    • First-order equations of motion for classical mechanics
    • R. Skinner, First-order equations of motion for classical mechanics, J. Math. Phys. 24 (1983) 2581-2588.
    • (1983) J. Math. Phys. , vol.24 , pp. 2581-2588
    • Skinner, R.1
  • 30
    • 36749118052 scopus 로고
    • Generalized hamiltonian dynamics. I. Formulation, on T* Q ⊕ TQ
    • R. Skinner and R. Rusk, Generalized hamiltonian dynamics. I. Formulation, on T* Q ⊕ TQ, J. Math. Phys. 24 (1983) 2589-2594.
    • (1983) J. Math. Phys. , vol.24 , pp. 2589-2594
    • Skinner, R.1    Rusk, R.2
  • 31
    • 0034697930 scopus 로고    scopus 로고
    • A new presymplectic geometrical framework for time-dependent lagrangian systems: The constraint algorithm and the second-order differential equation problem
    • S. Vignolo, A new presymplectic geometrical framework for time-dependent lagrangian systems: The constraint algorithm and the second-order differential equation problem, J. Phys. A: Math. Gen. 33 (2000) 5117-5135.
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 5117-5135
    • Vignolo, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.