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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F01%3A00000068%21RIV%2F2002%2FMSM%2F196102%2FN
rdf:type
skos:Concept n12:Vysledek
dcterms:description
A reformulation and generalization of basic concepts such as Hamiltonian system, Hamilton equations, regularity, and Legendre transformation for variational systems on fibered manifolds, is presented. The theory is based on the concept of Lepagean (n+1)-form (where n is the dimension of the base manifold). Contrary to the standard approach, where Hamiltonian theory is related to a single Lagrangian, here a Hamiltonian system is associated with an Euler-Lagrange form, i.e., with the class of all equivalent Lagrangians. Hamilton equations are introduced to be equations for integral sections of an exterior differential system. Relations between extremals and solutions of Hamilton equations are studied in detail. New regularity conditions and Legendre transformation formulas are found a procedure of regularization of variational problems is proposed. A reformulation and generalization of basic concepts such as Hamiltonian system, Hamilton equations, regularity, and Legendre transformation for variational systems on fibered manifolds, is presented. The theory is based on the concept of Lepagean (n+1)-form (where n is the dimension of the base manifold). Contrary to the standard approach, where Hamiltonian theory is related to a single Lagrangian, here a Hamiltonian system is associated with an Euler-Lagrange form, i.e., with the class of all equivalent Lagrangians. Hamilton equations are introduced to be equations for integral sections of an exterior differential system. Relations between extremals and solutions of Hamilton equations are studied in detail. New regularity conditions and Legendre transformation formulas are found a procedure of regularization of variational problems is proposed.
dcterms:title
Hamiltonian field theory revisited: A geometric approach to regularity Hamiltonian field theory revisited: A geometric approach to regularity
skos:prefLabel
Hamiltonian field theory revisited: A geometric approach to regularity Hamiltonian field theory revisited: A geometric approach to regularity
skos:notation
RIV/47813059:19610/01:00000068!RIV/2002/MSM/196102/N
n3:strany
187;207
n3:aktivita
n17:Z
n3:aktivity
Z(MSM 192400002)
n3:dodaniDat
n4:2002
n3:domaciTvurceVysledku
n11:4049160
n3:druhVysledku
n8:D
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n13:predkladatel
n3:idSjednocenehoVysledku
681451
n3:idVysledku
RIV/47813059:19610/01:00000068
n3:jazykVysledku
n7:eng
n3:klicovaSlova
Lagrangian systems; Poincaré-Cartan form; Lepagean form; Hamiltonian system; Hamilton extremals; Hamilton-DeDonder theory; Hamilton equations; regularity; Legendre transformations
n3:klicoveSlovo
n6:Lepagean%20form n6:Hamilton%20extremals n6:Poincar%C3%A9-Cartan%20form n6:Hamilton-DeDonder%20theory n6:regularity n6:Hamilton%20equations n6:Lagrangian%20systems n6:Hamiltonian%20system n6:Legendre%20transformations
n3:kontrolniKodProRIV
[F2113DA16224]
n3:mistoKonaniAkce
Debrecen
n3:mistoVydani
Debrecen
n3:nazevZdroje
Steps in Differential Geometry
n3:obor
n15:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:pocetUcastnikuAkce
0
n3:pocetZahranicnichUcastnikuAkce
0
n3:rokUplatneniVysledku
n4:2001
n3:tvurceVysledku
Krupková, Olga
n3:typAkce
n20:EUR
n3:zahajeniAkce
2000-01-01+01:00
n3:zamer
n16:MSM%20192400002
s:numberOfPages
21
n19:hasPublisher
Debrecen University
n10:organizacniJednotka
19610