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A relation between variational principles for equations of continuummechanics in Eulerian and Lagrangian descriptions is considered. It is shownthat for a system of differential equations in Eulerian variables correspondingLagrangian description is related to introducing nonlocal variables. Theconnection between these descriptions is obtained in terms of differentialcoverings. The relation between variational principles of a system of equationsand its symplectic structures is discussed. It is shown that if a system ofequations in Lagrangian variables can be derived from a variational principlethen there is no corresponding variational principle in Eulerian variables.

On the correspondence between variational principles in Eulerian and Lagrangian descriptions