Publication detail

On the Mayer problem II. Examples

CHRASTINOVÁ, V. TRYHUK, V.

Original Title

On the Mayer problem II. Examples

Type

journal article - other

Language

English

Original Abstract

Given an underdetermined system of ordinary differential equations, extremals of all possible variational problems relevant to the system together with the corresponding Poincar\'e--Cartan forms were characterized in geometrical terms in previous Part I of this article. The present Part II demonstrates the utility of this approach: it enables a deep insight into the structure of Euler--Lagrange and Hamilton--Jacobi equations not available by other methods and provides the sufficient extremality conditions without uncertain multipliers similar to the common Hilbert--Weierstrass theory. Degenerate variational problems are in principle not excluded and, like in the "royal road" by Carath\'eodory, no subtle investigation of admissible variations satisfying the boundary conditions is needed.

Keywords

diffiety, Mayer problem, Poincaré-Cartan module, Euler-Lagrange subspace, Hamilton--Jacobi equation

Authors

CHRASTINOVÁ, V.; TRYHUK, V.

RIV year

2002

Released

1. 1. 2002

Publisher

SAV

Location

Bratislava

ISBN

0139-9918

Periodical

Mathematica Slovaca

Year of study

52

Number

5

State

Slovak Republic

Pages from

571

Pages to

590

Pages count

20

BibTex

@article{BUT41270,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="On the Mayer problem II. Examples",
  journal="Mathematica Slovaca",
  year="2002",
  volume="52",
  number="5",
  pages="571--590",
  issn="0139-9918"
}