  A relation between variational principles for equations of continuum
mechanics in Eulerian and Lagrangian descriptions is considered. It is shown
that for a system of differential equations in Eulerian variables corresponding
Lagrangian description is related to introducing nonlocal variables. The
connection between these descriptions is obtained in terms of differential
coverings. The relation between variational principles of a system of equations
and its symplectic structures is discussed. It is shown that if a system of
equations in Lagrangian variables can be derived from a variational principle
then there is no corresponding variational principle in Eulerian variables.
