The Helmholtz conditions for systems of second order homogeneous differential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25530%2F13%3A39896095" target="_blank" >RIV/00216275:25530/13:39896095 - isvavai.cz</a>
Alternative codes found
RIV/61988987:17310/13:A1401A0H
Result on the web
<a href="http://dx.doi.org/10.5486/PMD.2013.5500" target="_blank" >http://dx.doi.org/10.5486/PMD.2013.5500</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5486/PMD.2013.5500" target="_blank" >10.5486/PMD.2013.5500</a>

Result language
angličtina
Original language name
The Helmholtz conditions for systems of second order homogeneous differential equations
Original language description
Variationality of systems of second order ordinary differential equations is studied within the class of positive homogeneous systems. The concept of a higher order positive homogeneous function, related to Finsler geometry, is represented by the well-known Zermelo conditions, and applied to the theory of variational equations. In particular, it is shown that every system of m+1 second order variational and positive homogeneous differential equations is linearly dependent and admits subsystems of m differential equations which are variational in sense of parameter-invariant variational problems, and vice versa. An example of a positive homogeneous variational system of second order differential equations is given.
Czech name
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Czech description
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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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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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