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rdf:type
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Description
| - In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems.
- In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems. (en)
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Title
| - Hamiltonian field theory
- Hamiltonian field theory (en)
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skos:prefLabel
| - Hamiltonian field theory
- Hamiltonian field theory (en)
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skos:notation
| - RIV/47813059:19610/02:00000084!RIV/2003/GA0/196103/N
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/00/0724), Z(MSM 192400002)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/47813059:19610/02:00000084
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Lagrangian; Poincaré-Cartan form; Lepagean n-form; Lepagean (n+1)-form; Hamilton extremal;Hamilton equations; Hamilton-De Donder equations; Regularity; Legendre transformation (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Journal of Geometry and Physics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...ocetUcastnikuAkce
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http://linked.open...nichUcastnikuAkce
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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