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The Poincaré-Cartan forms of one-dimensional variational integrals
Fundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincare-Cartan differential forms are ...
Pure mathematics
- 2020 •
- Jimp •
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On the Carathéodory form in higher-order variational field theory
operations applied to the well-known Poincaré-Cartan form and principal component of Lepage forms, respectively. For second-order theory, our definition coincidesThe Carathéodory form of the calculus of v...
Mathematics
- 2021 •
- Jimp •
- Link
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On regularization of variational problems in first-order field theory
Standard Hamiltonian formulation of field theory is founded upon the Poicaré-Cartan form. Accordingly, a first-order Lagrangian L is called regular if $det ({{pr^2 L} over {pr y^sigma_i pr y^nu_j}}) ne 0$; in this case the Hamilton ...
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
The symmetry reduction of variational integrals, complement
Some open problems appearing in the primary article on the symmetry reduction are solved.
Pure mathematics
- 2018 •
- Jimp •
- Link
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The symmetry reduction of variational integrals
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized...
Pure mathematics
- 2018 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Legendre transformation for regularizable Lagrangians in field theory
Hamilton equation based not only upon Poincaré-Cartan equivalent of a first order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton De Donder theory, but regularis...
BA - Obecná matematika
- 2002 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On Lepagean equivalents and multisymplectic forms
The paper is devoted to the case of the Lepagean and the multisymplectic forms whose~coming from the first order Lagrangian. Contrary to standard aproach we find new class of~multisymplectic forms which depend not only on given Lagr...
BA - Obecná matematika
- 2016 •
- D
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D - Stať ve sborníku
On Hamilton p2-equations in second order field theory
In the present paper recent results on regularizations of first order variational problems are generalized to Lagrangians affine in the second derivatives. New regularity conditions are found and Legendre transformations are studied....
BA - Obecná matematika
- 2001 •
- D
Rok uplatnění
D - Stať ve sborníku
The Regularization by Constant Functions of Lagrangians Linear in First Derivatives in Field Theory
forms are discussed.
Applied mathematics
- 2017 •
- D
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D - Stať ve sborníku
The fundamental Lepage form in two independent variables: a generalization using order-reducibility
) the principal component of Lepage form, extending the well-known Poincaré-Cartan formA second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifold...
Mathematics
- 2022 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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