Variational submanifolds of Euclidean spaces

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Variational submanifolds of Euclidean spaces
Original language description
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.
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
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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