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On the invariant variational sequences in mechanics. (English) Zbl 1028.58021
Bureš, Jarolím (ed.), The proceedings of the 22nd winter school “Geometry and physics”, Srní, Czech Republic, January 12-19, 2002. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 71, 185-190 (2003).
Summary: The $$r$$-th order variational sequence is the quotient sequence of the De Rham sequence on the $$r$$th jet prolongation of a fibered manifold, factored through its contact subsequence.
In this paper, the first order variational sequence on a fibered manifold with one-dimensional base is considered. A new representation of all quotient spaces as some spaces of (global) forms is given. The factorization procedure is based on a modification of the interior Euler operator, used in the theory of (infinite) variational bicomplexes.
For the entire collection see [Zbl 1014.00011].

##### MSC:
 58E30 Variational principles in infinite-dimensional spaces 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
##### Keywords:
first order variational sequence