| Title:
|
On the inverse variational problem in nonholonomic mechanics (English) |
| Author:
|
Rossi, Olga |
| Author:
|
Musilová, Jana |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
20 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
41-62 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with the recently found constraint Helmholtz conditions this result completes basic geometric properties of constraint variational systems. A few examples of constraint variational systems are discussed. (English) |
| Keyword:
|
inverse problem of the calculus of variations |
| Keyword:
|
Helmholtz conditions |
| Keyword:
|
nonholonomic constraints |
| Keyword:
|
the nonholonomic variational principle |
| Keyword:
|
constraint Euler-Lagrange equations |
| Keyword:
|
constraint Helmholtz conditions |
| Keyword:
|
constraint Lagrangian |
| Keyword:
|
constraint ballistic motion |
| Keyword:
|
relativistic particle |
| MSC:
|
49N45 |
| MSC:
|
58E30 |
| MSC:
|
70F25 |
| idZBL:
|
Zbl 06202718 |
| idMR:
|
MR3001631 |
| . |
| Date available:
|
2012-11-27T16:30:27Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143080 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
