Variational sequences on fibred velocity spaces

Zbynek Urban, Demeter Krupka

Abstract


The variational sequence theory in geometric mechanics is extended to second order velocity spaces oversmooth manifolds. New explicit formulas for the classes in this sequence, representing the variational objects such as Lagrangians,Euler-Lagrange forms and Helmholtz forms, are derived. The expressions, given in the canonical coordinates,explain the structure of trivial Lagrangians on these underlying manifolds and allow straightforward applications in theinverse problem of the calculus of variations. The differences between local and global variationality are discussed andillustrated by examples. The variational theory of parameter-invariant problems of second order is considered in terms ofjet differential groups.

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