Previous |  Up |  Next


Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lagrangian; Lepagean equivalents; Poincaré–Cartan form; regular and strongly regular systems
This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
[1] Dedecker, P.: On the generalization of symplectic geometry to multiple integrals in the calculus of variations. In: Lecture Notes in Math., 570, Springer, Berlin, 1977, 395–456. MR 0458478 | Zbl 0352.49018
[2] Gotay, M. J.: A multisymplectic framework for classical field theory and the calculus of variations, I. covariant Hamiltonian formalism. In: M., Francaviglia, D. D., Holm (eds.): Mechanics, Analysis and Geometry: 200 Years After Lagrange, North-Holland, Amsterdam, 1990, 203–235.
[3] Krupka, D.: Some geometric aspects of variational problems in fibered manifolds. Folia Fac. Sci. Nat. 14 (1973), 1–65.
[4] Krupka, D.: Lepagean forms in higher order variational theory. In: S., Benenti, M., Francaviglia, A., Lichnerowitz (eds.): Modern Developments in Analytical Mechanics I: Geometrical Dynamics, Proc. IUTAM-ISIM Symp., Accad. delle Scienze di Torino, Torino, 1983, 197–238. MR 0773488 | Zbl 0572.58003
[5] Krupková, O.: Hamiltonian field theory. J. Geom. Phys. 43 (2002), 93–132. DOI 10.1016/S0393-0440(01)00087-0 | MR 1919207 | Zbl 1016.37033
[6] Krupková, O.: Hamiltonian field theory revisited: A geometric approach to regularity. In: Steps in Differential Geometry, Proc. of the Coll. on Diff. Geom., University of Debrecen, Debrecen, 2001, 187–207. MR 1859298 | Zbl 0980.35009
[7] Krupková, O., Smetanová, D.: Legendre transformation for regularizable Lagrangians in field theory. Letters in Math. Phys. 58 (2001), 189–204. DOI 10.1023/A:1014548309187 | MR 1892919 | Zbl 1005.70025
[8] Saunders, D. J.: The Geometry of Jets Bundles. Cambridge University Press, Cambridge, 1989. MR 0989588
[9] Smetanová, D.: On regularization of second order Hamiltonian systems. Arch. Math. 42 (2006), 341–347. MR 2322420
[10] Smetanová, D.: On regularization of second order Lagrangians. In: Global Analysis and Applied Mathematics, American Institut of Physics, Proc. 729, Ankara, 2004, 289–296. MR 2215711 | Zbl 1119.35328
[11] Smetanová, D.: The second order lagrangians-regularity problem. In: 14th Conference on Applied Mathematics, APLIMAT 2015, STU Bratislava, Bratislava, 2015, 690–697.
Partner of
EuDML logo