Helmholtz conditions and their generalizations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F10%3AA13016BX" target="_blank" >RIV/61988987:17310/10:A13016BX - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Helmholtz conditions and their generalizations
Original language description
The Euler-Lagrange morphism E1 is well-understood. It is also known that the kernel of the Helmholtz morphism E2 consists of locally variational dynamical forms, and is characterized by Helmholtz conditions. We study the image of E2 and the kernel of thenext morphism E3, and solve the corresponding local and global inverse problem when a three-form comes from a dynamical form, i.e., corresponds to a system of diferential equations. We find identities, that are a generalization of the Helmholtz conditions to this situation, and show that the problem is closely related to the question on existence of a closed three-form. The obtained results extend known results on Lagrangians and locally variational dynamical forms to general dynamical forms, and opena new possibility to study non-variational equations by means of closed three-forms, as a parallel to extremal problems (variational equations) that are studied by means of closed two-forms (Cartan forms, symplectic geometry).
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Balkan Journal of Geometry and Its Applications
ISSN
1224-2780
e-ISSN
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Volume of the periodical
15
Issue of the periodical within the volume
1
Country of publishing house
RO - ROMANIA
Number of pages
10
Pages from-to
80-89
UT code for WoS article
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EID of the result in the Scopus database
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