Previous |  Up |  Next


Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
[1] Krupka D.: Some geometric aspects of variational problems in fibered manifolds. Folia Fac. Sci. Nat. UJEP Brunensis 14 (1973), 1–65.
[2] Krupková O.: Hamiltonian field theory. J. Geom. Phys. 43 (2002), 93–132. MR 1919207 | Zbl 1016.37033
[3] Krupková O.: Hamiltonian field theory revisited: A geometric approach to regularity. in: Steps in Differential Geometry, Proc. of the Coll. on Differential Geometry, Debrecen 2000 (University of Debrecen, Debrecen, 2001), 187–207. MR 1859298 | Zbl 0980.35009
[4] Krupková O.: Higher-order Hamiltonian field theory. Paper in preparation.
[5] Saunders D. J.: The geometry of jets bundles. Cambridge University Press, Cambridge, 1989. MR 0989588
[6] Shadwick W. F.: The Hamiltonian formulation of regular $r$-th order Lagrangian field theories. Lett. Math. Phys. 6 (1982), 409–416. MR 0685846
Partner of
EuDML logo