Displaying similar documents to “Jets and the variational calculus”

On the invariant variational sequences in mechanics

Šeděnková, Jana

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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...

Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents

Marcella Palese (2016)

Communications in Mathematics

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We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations...

Uniqueness results for operators in the variational sequence

W. M. Mikulski (2009)

Annales Polonici Mathematici

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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

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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...

The symmetry reduction of variational integrals

Václav Tryhuk, Veronika Chrastinová (2018)

Mathematica Bohemica

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The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the...