Detail publikačního výsledku

On the Mayer problem II. Examples

CHRASTINOVÁ, V.; TRYHUK, V.

Originální název

On the Mayer problem II. Examples

Anglický název

On the Mayer problem II. Examples

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

CHRASTINOVÁ, V.; TRYHUK, V.

Rok RIV

2011

Vydáno

01.01.2002

Nakladatel

SAV

Místo

Bratislava

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Svazek

52

Číslo

5

Stát

Slovenská republika

Strany od

571

Strany do

590

Strany počet

20

Plný text v Digitální knihovně

http://hdl.handle.net/

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"
}