Original title: Variational sequences in mechanics on Grassmann fibrations
Translated title: Variational sequences in mechanics on Grassmann fibrations
Authors: Urban, Zbyněk
Document type: Rigorous theses
Year: 2012
Language: eng
Abstract: [eng] [cze]
Extension of the variational sequence theory in mechanics to the Grassmann fibrations (prolongations) of 1-dimensional submanifolds is presented. The coordinate expressions of classes of differential forms, entering the variational sequence, are determined for arbitrary second order forms. In particular, the meaning of classes as the well-known variational objects (Lagrangian, Euler-Lagrange form, Helmholtz-Sonin form) is pointed out. 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. Tato práce se zabývá zobecněním teorie variační posloupnosti na Grassmannova prodloužení 1-rozměrných podvariet. Třídy diferenciálních forem, jakožto elementy variační posloupnosti, jsou určeny lokálně pro libovolné formy druhého řádu. Zabýváme se variačním významem tříd (Lagrangián, Eulerova-Lagrangeova forma, Helmholtzova-Soninova forma). Pomocí teorie jetů a kontaktních elementů ukazujeme vztah s variační teorií parametricky invariantních problémů.
Keywords: contact element; contact form; Euler-Lagrange equations; Grassmann fibration; Helmholtz conditions; jet; parameter-invariant variational theory; variational sequence; Eulerovy-Lagrangeovy rovnice; Grassmannova fibrace; Helmholtzovy podmínky; invariantní variační teorie; jet; kontaktní element; kontaktní forma; variační posloupnost

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/45358

Permalink: http://www.nusl.cz/ntk/nusl-440830


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Academic theses (ETDs) > Rigorous theses