SMETANOVÁ, Dana. Affine Lagrangians in Second Order Field Theory. In Jaromír Baštinec and Miroslav Hrubý. Mathematics, Information Technologies and Applied Sciences 2017. Mathematics, Information Tec. ČR: University of Defence, Brno, 2017. p. 217-225. ISBN 978-80-7582-026-6.
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Basic information
Original name Affine Lagrangians in Second Order Field Theory
Name in Czech Afinní lagrangiány v teorii pole 2. řádu
Authors SMETANOVÁ, Dana (203 Czech Republic, guarantor, belonging to the institution).
Edition Mathematics, Information Tec. ČR, Mathematics, Information Technologies and Applied Sciences 2017, p. 217-225, 9 pp. 2017.
Publisher University of Defence, Brno
Other information
Original language English
Type of outcome Proceedings paper
Field of Study 10100 1.1 Mathematics
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
Publication form electronic version available online
WWW URL
RIV identification code RIV/75081431:_____/17:00001860
Organization unit Institute of Technology and Business in České Budějovice
ISBN 978-80-7582-026-6
UT WoS 000576896800024
Keywords (in Czech) Lagrangián; Legendreova transformace; regularita; Hamiltonovy rovnice
Keywords in English Lagrangian; Legendre transformation; regularity; Hamilton equations
Tags MAT_2z, MAT_z, RIV20, WOS
Changed by Changed by: Kateřina Nygrýnová, učo 23736. Changed: 15/12/2020 16:43.
Abstract
In this paper we consider the extension of the classical Hamilton - Cartan variation theory to fibrous varieties. It is known that in field theory, we can assign various Hamiltonian equations corresponding to the Lepage equivalents of Lagrangian to the variational problem represented by Lagrangian. The case of affine Lagrangians in the second derivatives is studied using differential geometry tools. A new condition of regularity and strong regularity and Legendre's transformation are found.
Abstract (in Czech)
V příspěvku uvažujeme rozšíření klasické Hamiltonovy - Cartanovy variační teorie na fibrované variety. Je známo, že v teorii pole variačnímu problému reprezentovanému Lagrangiánem můžeme přiřadit různé Hamiltonovy rovnice koresponující s Lepageovými ekvivalenty lagrangiánu. Případ lagrangiánů afinních v druhých derivacích je studován za pomoci nástrojů diferenciální geometrie. Nalezeny jsou nová podmínka regularity a silné regularity a Legendrova transformace.
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