| Title:
|
Lepage forms theory applied (English) |
| Author:
|
Lenc, Michal |
| Author:
|
Musilová, Jana |
| Author:
|
Czudková, Lenka |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
279-287 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example. (English) |
| Keyword:
|
fibred manifold |
| Keyword:
|
Lagrangian |
| Keyword:
|
Lepage form |
| Keyword:
|
conservation laws |
| Keyword:
|
relativistic mechanics |
| MSC:
|
49Q20 |
| MSC:
|
49S05 |
| MSC:
|
53Z05 |
| MSC:
|
70H33 |
| idZBL:
|
Zbl 1212.49060 |
| idMR:
|
MR2591682 |
| . |
| Date available:
|
2009-12-22T07:53:09Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137460 |
| . |
| Reference:
|
[1] Krupka, D.: Global variational theory in fibred spaces. Handbook of global analysis (Krupka, D., Saunders, D., eds.), Elsevier, 2007, pp. 773–836. MR 2389646 |
| Reference:
|
[2] Krupková, O.: Mechanical systems with non-holonomic constraints.J. Math. Phys. 38 (1997), 5098–5126. MR 1471916, 10.1063/1.532196 |
| Reference:
|
[3] Krupková, O.: The Geometry of Ordinary Variational Equations.Lecture Notes in Math., vol. 1678, Springer, Berlin, 1997. MR 1484970 |
| Reference:
|
[4] Krupková, O., Musilová, J.: The relativistic particle as a mechanical system with non-holonomic constraints.J. Phys. A: Math. Gen. 34 (2001), 3859–3875. MR 1840850, 10.1088/0305-4470/34/18/313 |
| Reference:
|
[5] Musilová, J., Lenc, M.: Lepage forms in variational theories: From Lepage’s idea to the variational sequence.Variations, Geometry and Physics (2008), 1–31, O. Krupková and D. Saunders (Editors). Nova Science Publishers. MR 2523430 |
| Reference:
|
[6] Weinberg, S.: Cosmology.Oxford University Press, 2008. Zbl 1147.83002, MR 2410479 |
| . |
