| Title:
|
Invariant variational problems on principal bundles and conservation laws (English) |
| Author:
|
Brajerčík, Ján |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
357-366 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, we consider variational problems defined by $G$-invariant Lagrangians on the $r$-jet prolongation of a principal bundle $P$, where $G$ is the structure group of $P$. These problems can be also considered as defined on the associated bundle of the $r$-th order connections. The correspondence between the Euler-Lagrange equations for these variational problems and conservation laws is discussed. (English) |
| Keyword:
|
principal bundle |
| Keyword:
|
variational principle |
| Keyword:
|
invariant Lagrangian |
| Keyword:
|
Euler-Lagrange equations |
| Keyword:
|
Noether’s current |
| Keyword:
|
conservation law |
| MSC:
|
49Q99 |
| MSC:
|
49S05 |
| MSC:
|
58A10 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1265.49049 |
| idMR:
|
MR2876939 |
| . |
| Date available:
|
2011-12-16T15:24:09Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141783 |
| . |
| Reference:
|
[1] Brajerčík, J.: $Gl_{n} (\mathbb{R})$–invariant variational principles on frame bundles.Balkan J. Geom. Appl. 13 (1) (2008), 11–19. MR 2395370 |
| Reference:
|
[2] Brajerčík, J.: Order reduction of the Euler–Lagrange equations of higher order invariant variational problems on frame bundles.Czechoslovak Math. J. (2011), to appear. Zbl 1249.53029, MR 2886257, 10.1007/s10587-011-0048-4 |
| Reference:
|
[3] Brajerčík, J., Krupka, D.: Variational principles for locally variational forms.J. Math. Phys. 46 (2005), 1–15, 052903. Zbl 1110.58011, MR 2143003, 10.1063/1.1901323 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
