Displaying similar documents to “One version of Miron's geometry in Osc 3 M .”

On the invariant variational sequences in mechanics

Šeděnková, Jana

Similarity:

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...

Uniqueness results for operators in the variational sequence

W. M. Mikulski (2009)

Annales Polonici Mathematici

Similarity:

We prove that the most interesting operators in the Euler-Lagrange complex from the variational bicomplex in infinite order jet spaces are determined up to multiplicative constant by the naturality requirement, provided the fibres of fibred manifolds have sufficiently large dimension. This result clarifies several important phenomena of the variational calculus on fibred manifolds.

Solution of the inverse problem of the calculus of variations

Jan Chrastina (1994)

Mathematica Bohemica

Similarity:

Given a family of curves constituting the general solution of a system of ordinary differential equations, the natural question occurs whether the family is identical with the totality of all extremals of an appropriate variational problem. Assuming the regularity of the latter problem, effective approaches are available but they fail in the non-regular case. However, a rather unusual variant of the calculus of variations based on infinitely prolonged differential equations and systematic...

A Remark on Variational Principles of Choban, Kenderov and Revalski

Adrian Królak (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.