Variational sequences in mechanics on Grassmann Fibrations

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Authors	URBAN Zbyněk KRUPKA Demeter
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Acta Applicandae Mathematicae
MU Faculty or unit	Faculty of Science
Citation
Doi	http://dx.doi.org/10.1007/s10440-010-9561-y
Field	General mathematics
Keywords	Variational sequence; Euler-Lagrange equations; Helmholtz conditions; Jet
Description	Extension of the variational sequence theory in mechanics to the first order Grassmann fibrations of 1-dimensional submanifolds is presented. The correspondence with the variational theory of parameter-invariant problems on manifolds is discussed in terms of the theory of jets (slit tangent bundles) and contact elements. In particular, the Helmholtz expressions for parameter-invariant variational problems, measuring local variationality of differential forms and differential equations, are given in the canonical and adapted coordinates. The methods can easily be extended to higher order variational problems.
Related projects:	Global analysis and the geometry of fibred spaces