Publication detail

The Poincaré-Cartan forms of one-dimensional variational integrals

CHRASTINOVÁ, V. TRYHUK, V.

Original Title

The Poincaré-Cartan forms of one-dimensional variational integrals

English Title

The Poincaré-Cartan forms of one-dimensional variational integrals

Type

journal article in Web of Science

Language

en

Original Abstract

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

English abstract

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

Keywords

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

Released

10.12.2020

Publisher

Walter de Gruyter GmBH

Location

Berlin

ISBN

0139-9918

Periodical

Mathematica Slovaca

Year of study

70

Number

6

State

SK

Pages from

1381

Pages to

1412

Pages count

32

URL

Documents

BibTex


@article{BUT167533,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="The Poincaré-Cartan forms of one-dimensional variational integrals",
  annote="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",
  address="Walter de Gruyter GmBH",
  chapter="167533",
  doi="10.1515/ms-2017-0439",
  howpublished="print",
  institution="Walter de Gruyter GmBH",
  number="6",
  volume="70",
  year="2020",
  month="december",
  pages="1381--1412",
  publisher="Walter de Gruyter GmBH",
  type="journal article in Web of Science"
}