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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.

MSC:

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

Citations:

Zbl 1463.49055
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References:

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