| Title:
|
A geometric analysis of dynamical systems with singular Lagrangians (English) |
| Author:
|
Havelková, Monika |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
19 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
169-178 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics. (English) |
| Keyword:
|
singular Lagrangian systems |
| Keyword:
|
geometric constraint algorithm |
| Keyword:
|
extended dynamics |
| Keyword:
|
proper dynamics |
| Keyword:
|
final constraint submanifold higher order field theories |
| MSC:
|
37J05 |
| MSC:
|
51P05 |
| MSC:
|
70G45 |
| MSC:
|
70H03 |
| MSC:
|
70H45 |
| idZBL:
|
Zbl 1251.37052 |
| idMR:
|
MR2897268 |
| . |
| Date available:
|
2012-04-06T06:20:56Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142099 |
| . |
| Reference:
|
[1] Chinea, D., León, M. de, Marrero, J.C.: The constraint algorithm for time-dependent Lagrangians. J. Math. Phys. 35 1994 3410-3447 Zbl 0810.70014, MR 1279313, 10.1063/1.530476 |
| Reference:
|
[2] Dirac, P.A.M.: Generalized Hamiltonian dynamics. Canad. J. Math. II 1950 129-148 Zbl 0036.14104, MR 0043724, 10.4153/CJM-1950-012-1 |
| Reference:
|
[3] El-Zalan, H.A., Muslih, S.I., Elsabaa, F.M.F.: The Hamiltonian-Jacobi analysis of dynamical system with singular higher order Lagrangians. Hadronic Journal 30 2007 209-220 MR 2356437 |
| Reference:
|
[4] Goldschmidt, H., Sternberg, S.: The Hamilton-Cartan formalism in the calculus of variations. Ann. Inst. Fourier, Grenoble 23 1973 203-267 Zbl 0243.49011, MR 0341531, 10.5802/aif.451 |
| Reference:
|
[5] Gotay, M.J., Nester, J.M.: Presymplectic Lagrangian systems I: the constraint algorithm and the equivalence theorem. Ann. Inst. H. Poincaré Sect. A, 30 1979 129-142 Zbl 0414.58015, MR 0535369 |
| Reference:
|
[6] Gotay, M.J., Nester, J.M.: Presymplectic Lagrangian systems II: the second order equation problem. Ann. Inst. H. Poincaré Sect. A, 32 1980 1-13 Zbl 0453.58016, MR 0574809 |
| Reference:
|
[7] Gotay, M.J., Nester, J.M., Hinds, G.: Presymplectic manifolds and the Dirac-Bergmann theory of constraints. J. Math. Phys. 19 1978 2388-2399 Zbl 0418.58010, MR 0506712, 10.1063/1.523597 |
| Reference:
|
[8] Krupková, O.: A geometric setting for higher-order Dirac-Bergmann theory of constraints. J. Math. Phys. 35 1994 6557-6576 Zbl 0823.70016, MR 1303063, 10.1063/1.530691 |
| Reference:
|
[9] Krupková, O.: The Geometry of Ordinary Variational Equations. Springer 1997 MR 1484970 |
| Reference:
|
[10] Saunders, D.J.: The Geometry of Jet Bundles. Cambridge Univ. Press, Cambridge 2nd Ed. 2004 MR 0989588 |
| . |
