Lagrangian theory for presymplectic systems
Annales de l'I.H.P. Physique théorique, Volume 57 (1992) no. 1, p. 27-45
@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},
     publisher = {Gauthier-Villars},
     volume = {57},
     number = {1},
     year = {1992},
     pages = {27-45},
     zbl = {0760.58018},
     mrnumber = {1176356},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__57_1_27_0}
}
Muñoz Lecanda, M. C.; Roman Roy, N. Lagrangian theory for presymplectic systems. Annales de l'I.H.P. Physique théorique, Volume 57 (1992) no. 1, pp. 27-45. http://www.numdam.org/item/AIHPA_1992__57_1_27_0/

[1] P.A.M. Dirac, 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 43724 | Zbl 0036.14104

[2] P.G. Bergmann, Helv. Phys. Acta Suppl., IV, Vol. 79, 1956.

[3] A.J. Hanson, T. Regge and C. Teitelboim, Constraint Hamiltonian Systems, Academia Nazionale di Linzei, Rome, 1976.

[4] K. Sundermeyer, Constrained Dynamics, LNP, No. 169, Springer-Verlag, Berlin, 1982. | MR 678773 | Zbl 0508.58002

[5] R. Abraham and J.E. Marsden, Foundations of Mechanics, 2nd ed., Benjamin-Cummings, Reading (Ma), 1978. | MR 515141 | Zbl 0393.70001

[6] V. Arnold, Méthodes Mathématiques de la Mécanique Classique, Mir, Moscow, 1976. | MR 474391 | Zbl 0385.70001

[7] J. Klein, Espaces variationnels et Mécanique, Ann. Inst. Fourier, Grenoble, Vol. 12, 1962, pp. 1-124. | Numdam | MR 215269 | Zbl 0281.49026

[8] A. Weinstein, Lectures on Symplectic Manifolds, C.B.M.S. Regional Conf. Ser. Math., Vol. 29, 1979. | MR 598470 | Zbl 0406.53031

[9] M.J. Gotay, J.M. Nester and G. Hinds, Presymplectic Manifolds and the Dirac-Bergmann Theory of Constraints, J. Math. Phys., Vol. 19, 1978, pp. 2388-2399. | MR 506712 | Zbl 0418.58010

[10] J. Sniatycki, Dirac Brackets in Geometric Dynamics, Ann. Inst. H. Poincaré, Vol. A 20, 1978, pp. 365-372. | Numdam | MR 358860 | Zbl 0295.70010

[11] A. Licherowicz, Variété symplectique et dynamique associée à une sous-variété, C. R. Acad. Sci. Paris, T. 280, 1975, pp. 523-527. | MR 405503 | Zbl 0315.70016

[12] M.R. Menzio and W.M. Tulczyjew, Infinitesimal Symplectic Relations and Generalized Hamiltonian Dynamics, Ann. Inst. H. Poincaré, Vol. A 28, 1978, pp. 349-367. | Numdam | MR 511066 | Zbl 0405.58029

[13] J. Cariñena, J. Gomis, L.A. Ibort and N. Roman, Canonical Transformations Theory for Presymplectic Systems, J. Math. Phys., Vol. 26, (8), 1985, pp. 1961-1969. | MR 796226 | Zbl 0592.58018

[14] K. Kamimura, Singular Lagrangian and Constrained Hamiltonian Systems, Generalized Canonical Formalism, Nuov. Cim. B, Vol. 68, 1982, pp. 33-54. | MR 659816

[15] E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective, Wiley, N.Y., 1974. | MR 434047 | Zbl 0329.70001

[16] M.J. Gotay and J.M. Nester, Presymplectic Lagrangian Systems I: the Constraint Algorithm and the Equivalence Theorem, Ann. Inst. H. Poincaré, Vol. A 30, 1979, pp. 129-142. | Numdam | MR 535369 | Zbl 0414.58015

[17] R. Skinner and R. Rusk, 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 0556.70012

[18] G. Marmo, M. Mukunda and J. Samuel, Dynamics and Symmetry for Constrained Systems: a Geometrical Analysis, Riv. Nuov. Cim., Vol. 6, 1983. | MR 729476

[19] M. Crampin, Tangent Bundle Geometry for Lagrangian Dynamics. J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 3755-3772. | MR 727054 | Zbl 0536.58004

[20] M.J. Gotay and J.M. Nester, Presymplectic Lagrangian Systems II: the Second-Order Equation Problem, Ann. Inst. H. Poincaré, Vol. A 32, 1980, pp. 1-13. | Numdam | MR 574809 | Zbl 0453.58016

[21] C. Batlle, J. Gomis, J.M. Pons and N. Román-Roy, Equivalence Between the Lagrangian and Hamiltonian Formalism for Constrained Systems, J. Math. Phys., Vol. 27, (12), 1986, pp. 2953-2962. | MR 866595 | Zbl 0613.70012

[22] J.F. Cariñena, C. Lopez and N. Román-Roy, Geometric Study of the Connection Between the Lagrangian and Hamiltonian Constraints, J. Geom. Phys., Vol. 4, (3), 1987, pp. 315-334. | MR 957017 | Zbl 0657.58012

[23] C. Batlle, J. Gomis, J.M. Pons and N. Román, Lagrangian and Hamiltonian Constraints, Let. Math. Phys., Vol. 13, 1987, pp. 17-23. | MR 878657 | Zbl 0616.58015

[24] J.M. Pons, New Relations Between the Lagrangian and Hamiltonian Constraints, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 2705-2715. | MR 953447 | Zbl 0658.70016

[25] D. Bleecker, Gauge Theory and Variational Principles, Addison-Wesley, Reading (Ma), 1981. | MR 643361 | Zbl 0481.58002

[26] J.F. Cariñena, C. López and N. Román-Roy, Origin of the Lagrangian Constraints and their Relation with the Hamiltonian Formalism, J. Math. Phys., Vol. 29, (5), 1988, pp. 1143-1149. | MR 941034 | Zbl 0644.70013

[27] J.F. Cariñena and C. López, The Time Evolution Operator for Singular Lagrangians, Lett. Math. Phys., Vol. 14, 1987, pp. 203-210. | MR 919323 | Zbl 0638.58009

[28] X. Gràcia and J.M. Pons, On an Evolution Operator Connecting Lagrangian and Hamiltonian Formalisms, Lett. Math. Phys., Vol. 17, 1989, pp. 175-180. | MR 995795 | Zbl 0689.58016

[29] X. Gràcia and J.M. Pons, A Generalized Geometric Framework for Constrained Systems, Diff. Geom. Appl. (to appear) 1992. | MR 1245325 | Zbl 0763.34001

[30] M.C. Muñoz, Hamiltonian Constrained Systems: A Geometric Approach, Int. J. Theor. Phys., Vol. 28, 1989, pp. 1405-1417. | Zbl 0697.58019

[31] A. Besse, Manifolds all of Whose Geodesics Are Closed, Springer-Verlag, Berlin, 1980. | MR 496885 | Zbl 0387.53010

[32] S. Sternberg, Lectures on Differential Geometry, Chelsea Pub. Company, N.Y., 1983. | MR 891190 | Zbl 0518.53001

[33] C. Battle, J. Gomis, J.M. Pons and N. Román-Roy, On the Legendre Transformation for Singular Lagrangians and Related Topics, J. Phys. A: Math. Gen., Vol. 20, 1987, pp. 5113-5123. | MR 914696 | Zbl 0642.58029