Detail publikačního výsledku

The Poincaré-Cartan forms of one-dimensional variational integrals

CHRASTINOVÁ, V.; TRYHUK, V.

Originální název

The Poincaré-Cartan forms of one-dimensional variational integrals

Anglický název

The Poincaré-Cartan forms of one-dimensional variational integrals

Druh

Článek WoS

Originální abstrakt

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 relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually appears in full generality. It is presented from the differential forms point of view and does not require any intricate geometry. (C) 2020 Mathematical Institute Slovak Academy of Sciences

Anglický abstrakt

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 relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually appears in full generality. It is presented from the differential forms point of view and does not require any intricate geometry. (C) 2020 Mathematical Institute Slovak Academy of Sciences

Klíčová slova

Diffiety; variational integral; extremal; Lagrange variational problem; Poincaré-Cartan form; Euler-Lagrange system; integral invariant; Hamilton-Jacobi equation; exact inverse problem

Klíčová slova v angličtině

Diffiety; variational integral; extremal; Lagrange variational problem; Poincaré-Cartan form; Euler-Lagrange system; integral invariant; Hamilton-Jacobi equation; exact inverse problem

Autoři

CHRASTINOVÁ, V.; TRYHUK, V.

Rok RIV

2021

Vydáno

10.12.2020

Nakladatel

Walter de Gruyter GmBH

Místo

Berlin

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Svazek

70

Číslo

6

Stát

Slovenská republika

Strany od

1381

Strany do

1412

Strany počet

32

URL

https://www.x-mol.com/paper/1339684794756751360

BibTex

@article{BUT167533,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="The Poincaré-Cartan forms of one-dimensional variational integrals",
  journal="Mathematica Slovaca",
  year="2020",
  volume="70",
  number="6",
  pages="1381--1412",
  doi="10.1515/ms-2017-0439",
  issn="0139-9918",
  url="https://www.x-mol.com/paper/1339684794756751360"
}