On a global Lagrangian construction for ordinary variational equations on 2-manifolds

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27120%2F19%3A10242515" target="_blank" >RIV/61989100:27120/19:10242515 - isvavai.cz</a>
Výsledek na webu
<a href="https://aip.scitation.org/doi/10.1063/1.5100351" target="_blank" >https://aip.scitation.org/doi/10.1063/1.5100351</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.5100351" target="_blank" >10.1063/1.5100351</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On a global Lagrangian construction for ordinary variational equations on 2-manifolds
Popis výsledku v původním jazyce
Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, however, of sheaf-theoretic nature. A new constructive method of finding a global Lagrangian for second-order ODEs on 2-manifolds is described on the basis of the solvability of the exactness equation for the Lepage 2-forms and the top-cohomology theorems. Examples from geometry and mechanics are discussed.
Název v anglickém jazyce
On a global Lagrangian construction for ordinary variational equations on 2-manifolds
Popis výsledku anglicky
Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, however, of sheaf-theoretic nature. A new constructive method of finding a global Lagrangian for second-order ODEs on 2-manifolds is described on the basis of the solvability of the exactness equation for the Lepage 2-forms and the top-cohomology theorems. Examples from geometry and mechanics are discussed.

Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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