On a generalization of Helmholtz conditions
Acta Mathematica Universitatis Ostraviensis (2009)
- Volume: 17, Issue: 1, page 11-21
- ISSN: 1804-1388
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topMalíková, Radka. "On a generalization of Helmholtz conditions." Acta Mathematica Universitatis Ostraviensis 17.1 (2009): 11-21. <http://eudml.org/doc/35194>.
@article{Malíková2009,
abstract = {Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics ($n=1$), and obtain a generalization of Helmholtz conditions to this case.},
author = {Malíková, Radka},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Lagrangian; Euler-Lagrange form; dynamical form; Helmholtz-type form; Helmholtz form; Helmholtz conditions; Lagrangian; Euler-Lagrange form; dynamical form; Helmholtz-type form; Helmholtz conditions},
language = {eng},
number = {1},
pages = {11-21},
publisher = {University of Ostrava},
title = {On a generalization of Helmholtz conditions},
url = {http://eudml.org/doc/35194},
volume = {17},
year = {2009},
}
TY - JOUR
AU - Malíková, Radka
TI - On a generalization of Helmholtz conditions
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2009
PB - University of Ostrava
VL - 17
IS - 1
SP - 11
EP - 21
AB - Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics ($n=1$), and obtain a generalization of Helmholtz conditions to this case.
LA - eng
KW - Lagrangian; Euler-Lagrange form; dynamical form; Helmholtz-type form; Helmholtz form; Helmholtz conditions; Lagrangian; Euler-Lagrange form; dynamical form; Helmholtz-type form; Helmholtz conditions
UR - http://eudml.org/doc/35194
ER -
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