SOME ASPECTS OF VARIATIONAL SEQUENCES IN MECHANICS

Raffaele Vitolo

Key words: Fibred manifold, jet space, variational sequence,
        Euler--Lagrange map, Helmholtz map.

1991 Math. Subject Classification: 58A12, 58A20, 58E30, 58G05.

Abstract: We discuss intrinsic aspects of Krupka's approach
to finite--order variational sequences. We recover in an intrinsic
way the second--order variational calculus for  affine Lagrangians
by means of a natural generalisation of first--order theories.
Moreover, we find an intrinsic expression for the
Helmholtz morphism using a technique introduced by Kol\' a\v{r}
that we  have adapted to our context.