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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On a global Lagrangian construction for ordinary variational equations on 2-manifolds
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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