The symmetry reduction of variational integrals, complement

Abstract

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.

Keywords

• Lagrange variational problem
• Poincaré-Cartan form
• symmetry reduction