| Title:
|
On a generalization of Helmholtz conditions (English) |
| Author:
|
Malíková, Radka |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
17 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
11-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lagrangian |
| Keyword:
|
Euler-Lagrange form |
| Keyword:
|
dynamical form |
| Keyword:
|
Helmholtz-type form |
| Keyword:
|
Helmholtz form |
| Keyword:
|
Helmholtz conditions |
| MSC:
|
58A10 |
| MSC:
|
58A20 |
| MSC:
|
58E30 |
| MSC:
|
70G45 |
| idZBL:
|
Zbl 1238.58001 |
| idMR:
|
MR2582956 |
| . |
| Date available:
|
2010-03-08T21:26:23Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137524 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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