Druzhkov K. On the relation between symplectic structures and variational principles in continuum mechanics (abstract)

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Speaker: Konstantin Druzhkov

Title: On the relation between symplectic structures and variational principles in continuum mechanics

Abstract:
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.


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.