On Lagrangians with reduced-order Euler–Lagrange equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA20022E8" target="_blank" >RIV/61988987:17310/18:A20022E8 - isvavai.cz</a>
Result on the web
<a href="https://www.emis.de/journals/SIGMA/2018/089/sigma18-089.pdf" target="_blank" >https://www.emis.de/journals/SIGMA/2018/089/sigma18-089.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3842/SIGMA.2018.089" target="_blank" >10.3842/SIGMA.2018.089</a>
Alternative languages
Result language
angličtina
Original language name
On Lagrangians with reduced-order Euler–Lagrange equations
Original language description
If a Lagrangian defining a variational problem has order k then its Euler-Lagrange equations generically have order 2k. This paper considers the case where the Euler-Lagrange equations have order strictly less than 2k, and shows that in such a case the Lagrangian must be a polynomial in the highest-order derivative variables, with a specific upper bound on the degree of the polynomial. The paper also provides an explicit formulation, derived from a geometrical construction, of a family of such k-th order Lagrangians, and it is conjectured that all such Lagrangians arise in this way.
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
ISSN
1815-0659
e-ISSN
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Volume of the periodical
14
Issue of the periodical within the volume
Srpen
Country of publishing house
UA - UKRAINE
Number of pages
13
Pages from-to
089
UT code for WoS article
000443332100001
EID of the result in the Scopus database
2-s2.0-85052739793