Druzhkov K. On the relation between symplectic structures and variational principles in continuum mechanics (abstract): Difference between revisions
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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. | 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. | ||
| video = https://video.gdeq.org/AMV-conf-20211214-Konstantin_Druzhkov.mp4 | |||
| slides = [[Media:DruzhkovAMVconf2021slides.pdf|DruzhkovAMVconf2021slides.pdf]] | | slides = [[Media:DruzhkovAMVconf2021slides.pdf|DruzhkovAMVconf2021slides.pdf]] | ||
| references = | | references = | ||
| event = [[Diffieties, Cohomological Physics, and Other Animals]], 13-17 December 2021, Moscow.<br>''Alexandre Vinogradov Memorial Conference.'' | | event = [[Diffieties, Cohomological Physics, and Other Animals]], 13-17 December 2021, Moscow.<br>''Alexandre Vinogradov Memorial Conference.'' | ||
| 79YY-MM-DD = 7978-87- | | 79YY-MM-DD = 7978-87-85 | ||
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Latest revision as of 08:40, 4 January 2025
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.
Video
Slides: DruzhkovAMVconf2021slides.pdf
Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.