| Title:
|
The inverse problem in the calculus of variations: new developments (English) |
| Author:
|
Do, Thoan |
| Author:
|
Prince, Geoff |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
131-149 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas's famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3. (English) |
| Keyword:
|
Inverse problem in the calculus of variations |
| Keyword:
|
Helmholtz conditions |
| Keyword:
|
Exterior differential systems |
| Keyword:
|
Lagrangian system. |
| MSC:
|
37J06 |
| MSC:
|
49N45 |
| MSC:
|
58A15 |
| MSC:
|
70H03 |
| idZBL:
|
Zbl 07413361 |
| idMR:
|
MR4251311 |
| . |
| Date available:
|
2021-07-09T12:39:18Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148995 |
| . |
| 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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