# On second order Hamiltonian systems

Archivum Mathematicum (2006)

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

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topSmetanová, 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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- 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
- Krupková O., Higher-order Hamiltonian field theory, Paper in preparation.
- Saunders D. J., The geometry of jets bundles, Cambridge University Press, Cambridge, 1989. (1989) MR0989588
- 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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