The symmetry reduction of variational integrals, complement. (English) Zbl 1463.49054

Summary: Some open problems appearing in the primary article [the authors, ibid. 143, No. 3, 291–328 (2018; Zbl 1463.49055)] 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.


49S05 Variational principles of physics
49N99 Miscellaneous topics in calculus of variations and optimal control
70H03 Lagrange’s equations


Zbl 1463.49055
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