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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:
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


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