Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-f...
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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148385 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations / O. Constantinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1483852019-02-19T01:25:44Z Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations Constantinescu, O. We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that P is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor R of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds. 2012 Article Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations / O. Constantinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 49N45; 58E30; 34A26; 37J30 DOI: http://dx.doi.org/10.3842/SIGMA.2012.059 http://dspace.nbuv.gov.ua/handle/123456789/148385 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that P is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor R of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds. |
| format |
Article |
| author |
Constantinescu, O. |
| spellingShingle |
Constantinescu, O. Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Constantinescu, O. |
| author_sort |
Constantinescu, O. |
| title |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations |
| title_short |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations |
| title_full |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations |
| title_fullStr |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations |
| title_full_unstemmed |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations |
| title_sort |
formal integrability for the nonautonomous case of the inverse problem of the calculus of variations |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148385 |
| citation_txt |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations / O. Constantinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT constantinescuo formalintegrabilityforthenonautonomouscaseoftheinverseproblemofthecalculusofvariations |
| first_indexed |
2023-05-20T17:30:37Z |
| last_indexed |
2023-05-20T17:30:37Z |
| _version_ |
1796153463977017344 |