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A note to the representation of the variational sequence
in mechanics

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*Jana Musilová and Michael Krbek*

**E-mail:** janam@physics.muni.cz
**Abstract.** The problem of the representation of the physically
important terms in the variational sequence in the higher order mechanics
(Euler-Lagrange and Helmholtz-Sonin mappings) is completely solved in the
local case. The physically adequate representation of classes of $1-$forms,
$2-$forms and $3-$forms is found. Moreover, the conditions for recognizing
the forms which play the role of representatives of classes in the variational
sequence are given. Finally, the complete reconstruction of classes of
forms based on the knowledge of the representative is presented.

**AMSclassification.** 49F05, 58A15, 58E99

**Keywords.** Fibered manifold, $r$--jet prolongation, variational
sequence, Lagrange structure, Euler--Lagrange mapping, Helmholtz--Sonin
mapping