Variational submanifolds of Euclidean spaces
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27120%2F18%3A10240044" target="_blank" >RIV/61989100:27120/18:10240044 - isvavai.cz</a>
Výsledek na webu
<a href="https://aip.scitation.org/doi/10.1063/1.5010221" target="_blank" >https://aip.scitation.org/doi/10.1063/1.5010221</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.5010221" target="_blank" >10.1063/1.5010221</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Variational submanifolds of Euclidean spaces
Popis výsledku v původním jazyce
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.
Název v anglickém jazyce
Variational submanifolds of Euclidean spaces
Popis výsledku anglicky
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of Mathematical Physics
ISSN
0022-2488
e-ISSN
—
Svazek periodika
59
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
20
Strana od-do
—
Kód UT WoS článku
000428902300029
EID výsledku v databázi Scopus
2-s2.0-85044711311