Výsledky vyhledávání - "Urban, Zbyněk"

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The fundamental Lepage form in two independent variables: a generalization using order-reducibility

A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) equivalence relation "Lepage differential 2-form is closed if an

Externí odkaz: http://arxiv.org/abs/2204.01663

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On the Carath\'eodory form in higher-order variational field theory

Autor: Urban, Zbyněk, Volná, Jana

The Carath\'eodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrisic geometric

Externí odkaz: http://arxiv.org/abs/2104.03609

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The Noether Bessel Hagen Symmetry Approach for Dynamical Systems

Autor: Urban, Zbynek, Bajardi, Francesco, Capozziello, Salvatore

The Noether-Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the No

Externí odkaz: http://arxiv.org/abs/2003.13756

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Exactness of Lepage 2-forms and globally variational differential equations

Autor: Urban, Zbynek, Volna, Jana

Publikováno v: Int. J. Geom. Meth. Mod. Phys. 16, No. Supp02 (2019) 1950106

The exactness equation for Lepage 2-forms, associated with variational systems of ordinary differential equations on smooth manifolds, is analyzed with the aim to construct a concrete global variational principle. It is shown that locally variational

Externí odkaz: http://arxiv.org/abs/1909.05115

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On a global Lagrangian construction for ordinary variational equations on 2-manifolds

Autor: Urban, Zbyněk, Volná, Jana

Publikováno v: J. Math. Phys. 60, 092902 (2019)

Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic nature. A new

Externí odkaz: http://arxiv.org/abs/1812.04270

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The fundamental Lepage form in variational theory for submanifolds

Autor: Urban, Zbyněk, Brajerčík, Ján

Publikováno v: International Journal of Geometric Methods in Modern Physics Vol. 15, No. 6 (2018) 1850103

A setting for global variational geometry on Grassmann fibrations is presented. The integral variational functionals for finite dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous Lagrangian, w

Externí odkaz: http://arxiv.org/abs/1709.08345

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Variational submanifolds of Euclidean spaces

Autor: Krupka, Demeter, Urban, Zbyněk, Volná, Jana

Publikováno v: Journal of Mathematical Physics 59, 032903 (2018)

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational s

Externí odkaz: http://arxiv.org/abs/1709.07826

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