ИСТИНА

The relation between symplectic structures and variational principles of equations in an extended Kovalevskaya form is considered. It is shown that each symplectic structure of a system of equations in an extended Kovalevskaya form determines a variational principle. A canonical way to derive variational principle from a symplectic structure is obtained. The relation between variational principles in Eulerian and Lagrangian variables is discussed. It is shown that if a system of equations in Lagrangian variables is an Euler-Lagrange system of equations, then the corresponding variational principle has no analogues in Eulerian variables