@article{AIHPA_1992__57_1_27_0, author = {Mu\~noz Lecanda, M. C. and Roman Roy, N.}, title = {Lagrangian theory for presymplectic systems}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {27--45}, publisher = {Gauthier-Villars}, volume = {57}, number = {1}, year = {1992}, mrnumber = {1176356}, zbl = {0760.58018}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1992__57_1_27_0/} }
TY - JOUR AU - Muñoz Lecanda, M. C. AU - Roman Roy, N. TI - Lagrangian theory for presymplectic systems JO - Annales de l'I.H.P. Physique théorique PY - 1992 SP - 27 EP - 45 VL - 57 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1992__57_1_27_0/ LA - en ID - AIHPA_1992__57_1_27_0 ER -
Muñoz Lecanda, M. C.; Roman Roy, N. Lagrangian theory for presymplectic systems. Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 1, pp. 27-45. http://archive.numdam.org/item/AIHPA_1992__57_1_27_0/
[1] Generalized Hamiltonian Mechanics, Can. J. Math., Vol. 2, 1950, pp. 129-148, and Lect. Quantum Mechanics, Belfer Graduate School of Science Monograph Series, Vol. 2, Yeshiva Univ., 1964. | MR | Zbl
,[2] Helv. Phys. Acta Suppl., IV, Vol. 79, 1956.
,[3] Constraint Hamiltonian Systems, Academia Nazionale di Linzei, Rome, 1976.
, and ,[4] Constrained Dynamics, LNP, No. 169, Springer-Verlag, Berlin, 1982. | MR | Zbl
,[5] Foundations of Mechanics, 2nd ed., Benjamin-Cummings, Reading (Ma), 1978. | MR | Zbl
and ,[6] Méthodes Mathématiques de la Mécanique Classique, Mir, Moscow, 1976. | MR | Zbl
,[7] Espaces variationnels et Mécanique, Ann. Inst. Fourier, Grenoble, Vol. 12, 1962, pp. 1-124. | Numdam | MR | Zbl
,[8] Lectures on Symplectic Manifolds, C.B.M.S. Regional Conf. Ser. Math., Vol. 29, 1979. | MR | Zbl
,[9] Presymplectic Manifolds and the Dirac-Bergmann Theory of Constraints, J. Math. Phys., Vol. 19, 1978, pp. 2388-2399. | MR | Zbl
, and ,[10] Dirac Brackets in Geometric Dynamics, Ann. Inst. H. Poincaré, Vol. A 20, 1978, pp. 365-372. | Numdam | MR | Zbl
,[11] Variété symplectique et dynamique associée à une sous-variété, C. R. Acad. Sci. Paris, T. 280, 1975, pp. 523-527. | MR | Zbl
,[12] Infinitesimal Symplectic Relations and Generalized Hamiltonian Dynamics, Ann. Inst. H. Poincaré, Vol. A 28, 1978, pp. 349-367. | Numdam | MR | Zbl
and ,[13] Canonical Transformations Theory for Presymplectic Systems, J. Math. Phys., Vol. 26, (8), 1985, pp. 1961-1969. | MR | Zbl
, , and ,[14] Singular Lagrangian and Constrained Hamiltonian Systems, Generalized Canonical Formalism, Nuov. Cim. B, Vol. 68, 1982, pp. 33-54. | MR
,[15] Classical Dynamics: A Modern Perspective, Wiley, N.Y., 1974. | MR | Zbl
and ,[16] Presymplectic Lagrangian Systems I: the Constraint Algorithm and the Equivalence Theorem, Ann. Inst. H. Poincaré, Vol. A 30, 1979, pp. 129-142. | Numdam | MR | Zbl
and ,[17] Generalized Hamiltonian Dynamics I: Formulation on T*Q⊕TQ, J. Math. Phys., Vol. 24, (11), 1983, pp. 2589-2594; and Generalized Hamiltonian Dynamics II: Gauge Transformations, J. Math. Phys., Vol. 24, (11), 1983, pp. 2595-2601. | Zbl
and ,[18] Dynamics and Symmetry for Constrained Systems: a Geometrical Analysis, Riv. Nuov. Cim., Vol. 6, 1983. | MR
, and ,[19] Tangent Bundle Geometry for Lagrangian Dynamics. J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 3755-3772. | MR | Zbl
,[20] Presymplectic Lagrangian Systems II: the Second-Order Equation Problem, Ann. Inst. H. Poincaré, Vol. A 32, 1980, pp. 1-13. | Numdam | MR | Zbl
and ,[21] Equivalence Between the Lagrangian and Hamiltonian Formalism for Constrained Systems, J. Math. Phys., Vol. 27, (12), 1986, pp. 2953-2962. | MR | Zbl
, , and ,[22] Geometric Study of the Connection Between the Lagrangian and Hamiltonian Constraints, J. Geom. Phys., Vol. 4, (3), 1987, pp. 315-334. | MR | Zbl
, and ,[23] Lagrangian and Hamiltonian Constraints, Let. Math. Phys., Vol. 13, 1987, pp. 17-23. | MR | Zbl
, , and ,[24] New Relations Between the Lagrangian and Hamiltonian Constraints, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 2705-2715. | MR | Zbl
,[25] Gauge Theory and Variational Principles, Addison-Wesley, Reading (Ma), 1981. | MR | Zbl
,[26] Origin of the Lagrangian Constraints and their Relation with the Hamiltonian Formalism, J. Math. Phys., Vol. 29, (5), 1988, pp. 1143-1149. | MR | Zbl
, and ,[27] The Time Evolution Operator for Singular Lagrangians, Lett. Math. Phys., Vol. 14, 1987, pp. 203-210. | MR | Zbl
and ,[28] On an Evolution Operator Connecting Lagrangian and Hamiltonian Formalisms, Lett. Math. Phys., Vol. 17, 1989, pp. 175-180. | MR | Zbl
and ,[29] A Generalized Geometric Framework for Constrained Systems, Diff. Geom. Appl. (to appear) 1992. | MR | Zbl
and ,[30] Hamiltonian Constrained Systems: A Geometric Approach, Int. J. Theor. Phys., Vol. 28, 1989, pp. 1405-1417. | Zbl
,[31] Manifolds all of Whose Geodesics Are Closed, Springer-Verlag, Berlin, 1980. | MR | Zbl
,[32] Lectures on Differential Geometry, Chelsea Pub. Company, N.Y., 1983. | MR | Zbl
,[33] On the Legendre Transformation for Singular Lagrangians and Related Topics, J. Phys. A: Math. Gen., Vol. 20, 1987, pp. 5113-5123. | MR | Zbl
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