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Invariance properties of classes in the variational sequence suggested toKrupka et al. the idea that there should exist a close correspondence betweenthe notions of variationality of a differential form and invariance of itsexterior derivative. It was shown by them that the invariance of a closedHelmholtz form of a dynamical form is equivalent with local variationality ofthe Lie derivative of the dynamical form, so that the latter is locally theEuler--Lagrange form of a Lagrangian. We show that the corresponding localsystem of Euler--Lagrange forms is variationally equivalent to a globalEuler--Lagrange form.

Symmetries of Helmholtz forms and globally variational dynamical forms