| Title:
|
On second order Hamiltonian systems (English) |
| Author:
|
Smetanová, Dana |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
341-347 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Euler–Lagrange equations |
| Keyword:
|
Hamiltonian systems |
| Keyword:
|
Hamilton extremals |
| Keyword:
|
Dedecker–Hamilton extremals |
| Keyword:
|
Hamilton equations |
| Keyword:
|
Lepagean equivalents |
| MSC:
|
37J05 |
| MSC:
|
58E30 |
| MSC:
|
70S05 |
| idZBL:
|
Zbl 1164.35304 |
| idMR:
|
MR2322420 |
| . |
| Date available:
|
2008-06-06T22:50:09Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108040 |
| . |
| Reference:
|
[1] Krupka D.: Some geometric aspects of variational problems in fibered manifolds.Folia Fac. Sci. Nat. UJEP Brunensis 14 (1973), 1–65. |
| Reference:
|
[2] Krupková O.: Hamiltonian field theory.J. Geom. Phys. 43 (2002), 93–132. Zbl 1016.37033, MR 1919207 |
| Reference:
|
[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. Zbl 0980.35009, MR 1859298 |
| Reference:
|
[4] Krupková O.: Higher-order Hamiltonian field theory.Paper in preparation. |
| Reference:
|
[5] Saunders D. J.: The geometry of jets bundles.Cambridge University Press, Cambridge, 1989. MR 0989588 |
| Reference:
|
[6] Shadwick W. F.: The Hamiltonian formulation of regular $r$-th order Lagrangian field theories.Lett. Math. Phys. 6 (1982), 409–416. MR 0685846 |
| . |
