On second order Hamiltonian systems

Dana Smetanová

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 341-347
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Smetanová, Dana. "On second order Hamiltonian systems." Archivum Mathematicum 042.5 (2006): 341-347. <http://eudml.org/doc/249805>.

@article{Smetanová2006,
abstract = {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.},
author = {Smetanová, Dana},
journal = {Archivum Mathematicum},
keywords = {Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents; Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents},
language = {eng},
number = {5},
pages = {341-347},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On second order Hamiltonian systems},
url = {http://eudml.org/doc/249805},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Smetanová, Dana
TI - On second order Hamiltonian systems
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 341
EP - 347
AB - 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.
LA - eng
KW - Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents; Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents
UR - http://eudml.org/doc/249805
ER -

References

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  1. Krupka D., Some geometric aspects of variational problems in fibered manifolds, Folia Fac. Sci. Nat. UJEP Brunensis 14 (1973), 1–65. (1973) 
  2. Krupková O., Hamiltonian field theory, J. Geom. Phys. 43 (2002), 93–132. Zbl1016.37033MR1919207
  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. Zbl0980.35009MR1859298
  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. (1989) MR0989588
  6. Shadwick W. F., The Hamiltonian formulation of regular r -th order Lagrangian field theories, Lett. Math. Phys. 6 (1982), 409–416. (1982) MR0685846

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