Displaying similar documents to “On the equivalence of variational problems. II”

A new infinite order formulation of variational sequences

Raffaele Vitolo (1998)

Archivum Mathematicum

Similarity:

The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the...

On a generalization of Helmholtz conditions

Radka Malíková (2009)

Acta Mathematica Universitatis Ostraviensis

Similarity:

Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics ( n = 1 ), and obtain a generalization of Helmholtz conditions to this case. ...