Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
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| Creator |
Constantinescu, O.
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| 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.
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| Date |
2019-02-18T11:18:45Z
2019-02-18T11:18:45Z 2012 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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