| Title:
|
The symmetry reduction of variational integrals, complement (English) |
| Author:
|
Chrastinová, Veronika |
| Author:
|
Tryhuk, Václav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
431-439 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning. (English) |
| Keyword:
|
Lagrange variational problem |
| Keyword:
|
Poincaré-Cartan form |
| Keyword:
|
symmetry reduction |
| MSC:
|
49N99 |
| MSC:
|
49S05 |
| MSC:
|
70H03 |
| idZBL:
|
Zbl 06997376 |
| idMR:
|
MR3895266 |
| DOI:
|
10.21136/MB.2018.0111-17 |
| . |
| Date available:
|
2018-11-29T09:26:04Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147479 |
| . |
| Reference:
|
[1] Bažaňski, S. L.: The Jacobi variational principle revisited.Classical and Quantum Integrability Banach Cent. Publ. 59. Polish Academy of Sciences, Institute of Mathematics, Warsaw (2003), 99-111 J. Grabowski et al. Zbl 1082.70008, MR 2003718, 10.4064/bc59-0-4 |
| Reference:
|
[2] Chrastinová, V.: The Intransitive Lie Group Actions with Variable Structure Constants.Mathematics, Information Technologies and Applied Sciences 2017 University of Defence, Brno (2017), 141-146 J. Baštinec et al. |
| Reference:
|
[3] Hermann, R.: Differential form methods in the theory of variational systems and Lagrangian field theories.Acta Appl. Math. 12 (1988), 35-78. Zbl 0664.49018, MR 0962880, 10.1007/BF00047568 |
| Reference:
|
[4] Langerock, B., Cantrijn, F., Vankerschaver, J.: Routhian reduction for quasi-invariant Lagrangians.J. Math. Phys. 51 (2010), Paper No. 022902, 20 pages. Zbl 1309.70019, MR 2605045, 10.1063/1.3277181 |
| Reference:
|
[5] Olver, P. J., Pohjanpelto, J., Valiquette, F.: On the structure of Lie pseudo-groups.SIGMA, Symmetry Integrability Geom. Methods Appl. 5 (2009), Paper No. 077, 14 pages. Zbl 1241.58008, MR 2529170, 10.3842/SIGMA.2009.077 |
| Reference:
|
[6] Tryhuk, V., Chrastinová, V.: On the internal approach to differential equations 1. The involutiveness and standard basis.Math. Slovaca 66 (2016), 999-1018. Zbl 06662105, MR 3567912, 10.1515/ms-2015-0198 |
| Reference:
|
[7] Tryhuk, V., Chrastinová, V.: The symmetry reduction of variational integrals.Math. Bohemica 143 (2018), 291-328. Zbl 06940885, MR 3852296, 10.21136/MB.2017.0008-17 |
| . |
