Geodesic
The symmetry reduction of variational integrals, complement
Mathematica Bohemica, Tome 143 (2018) no. 4, pp. 431-439
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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.
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.
DOI : 10.21136/MB.2018.0111-17
Classification : 49N99, 49S05, 70H03
Keywords: Lagrange variational problem; Poincaré-Cartan form; symmetry reduction 
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Chrastinová, Veronika; Tryhuk, Václav. The symmetry reduction of variational integrals, complement. Mathematica Bohemica, Tome 143 (2018) no. 4, pp. 431-439. doi: 10.21136/MB.2018.0111-17

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