Variational Sequences in Mechanics on Grassmann Fibrations |
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Authors: | Zbyněk Urban Demeter Krupka |
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Institution: | 1.Department of Algebra and Geometry,Palacky University in Olomouc,Olomouc,Czech Republic;2.Institute of Theoretical Physics and Astrophysics,Masaryk University in Brno,Brno,Czech Republic;3.Department of Mathematics,La Trobe University,Melbourne,Australia |
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Abstract: | 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. |
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Keywords: | |
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