| Title:
|
On the inverse problem of the calculus of variations for ordinary differential equations (English) |
| Author:
|
Krupková, Olga |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
261-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given. (English) |
| Keyword:
|
Lepagean forms |
| Keyword:
|
variational equations |
| Keyword:
|
Helmholtz conditions |
| Keyword:
|
minimal- order Lagrangian |
| Keyword:
|
local inverse problem to the calculus of variations |
| Keyword:
|
global inverse problem to the calculus of variations |
| MSC:
|
49N45 |
| MSC:
|
58E30 |
| MSC:
|
58F05 |
| MSC:
|
70H03 |
| MSC:
|
70H35 |
| idZBL:
|
Zbl 0786.58012 |
| idMR:
|
MR1239121 |
| DOI:
|
10.21136/MB.1993.125932 |
| . |
| Date available:
|
2009-09-24T20:59:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125932 |
| . |
| 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:
|
[8] D. Krupkа: Lepagean forms in higher order variational theory.in: Modern Developments in Analytical Mechanics I: Geometrical Dynamics, Pгoc. IUTAM-ISIMM Symposium, Torino, Italy, 1982 (S. Benenti, M. Francaviglia and A. Lichnerowicz, eds.), Accad. delle Scienze di Torino, Torino, 1983, pp. 197-238. MR 0773488 |
| 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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| Reference:
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| . |
