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Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
Інший ID:
2010 Mathematics Subject Classification: 49N45; 58E30; 34A26; 37J30
DOI: http://dx.doi.org/10.3842/SIGMA.2012.059
DOI: http://dx.doi.org/10.3842/SIGMA.2012.059
Посилання:
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.
Підтримка:
The author express his thanks to Ioan Bucataru for the many interesting discussions about the pape
Дата:
2012
Переглядів:
511
Завантажень:
219
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
Анотація:
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.
