Variational sequences in mechanics on Grassmann Fibrations

• Autoři: URBAN Zbyněk; KRUPKA Demeter
• Rok publikování: 2010
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Acta Applicandae Mathematicae
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1007/s10440-010-9561-y
• Obor: Obecná matematika
• Klíčová slova: Variational sequence; Euler-Lagrange equations; Helmholtz conditions; Jet
• Popis: 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.

Související projekty

• Globální analýza a geometrie fibrovaných prostorů