| Title:
|
Symmetries of a dynamical system represented by singular Lagrangians (English) |
| Author:
|
Havelková, Monika |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
20 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
23-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dynamical properties of singular Lagrangian systems differ from those of classical Lagrangians of the form $L=T-V$. Even less is known about symmetries and conservation laws of such Lagrangians and of their corresponding actions. In this article we study symmetries and conservation laws of a concrete singular Lagrangian system interesting in physics. We solve the problem of determining all point symmetries of the Lagrangian and of its Euler-Lagrange form, i.e. of the action. It is known that every point symmetry of a Lagrangian is a point symmetry of its Euler-Lagrange form, and this of course happens also in our case. We are also interested in the converse statement, namely if to every point symmetry $\xi$ of the Euler-Lagrange form $E$ there exists a Lagrangian $\lambda$ for $E$ such that $\xi$ is a point symmetry of $\lambda$. In the case studied the answer is affirmative, moreover we have found that the corresponding Lagrangians are all of order one. (English) |
| Keyword:
|
singular Lagrangians |
| Keyword:
|
Euler-Lagrange form |
| Keyword:
|
point symmetry |
| Keyword:
|
conservation law |
| Keyword:
|
equivalent Lagrangians |
| MSC:
|
70H03 |
| MSC:
|
70H33 |
| MSC:
|
70H45 |
| idZBL:
|
Zbl 06202716 |
| idMR:
|
MR3001629 |
| . |
| Date available:
|
2012-11-27T16:28:31Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143078 |
| . |
| Reference:
|
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