Examples from the calculus of variations. I. Nondegenerate problems

Title:

Examples from the calculus of variations. I. Nondegenerate problems

Creator:

Chrastina, Jan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e6377ab2-53c6-4f15-8437-aa4cc683a351
uuid:e6377ab2-53c6-4f15-8437-aa4cc683a351
doi:10.21136/MB.2000.126263

Subject:

variational integral, critical curve, adjoint module, initial form, Poincaré-Cartan form, Lagrange problem, Mayer field, Weierstrass function, and diffiety

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling the common Euler-Lagrange, Legendre, Jacobi, and Hilbert-Weierstrass conditions whenever possible and to discuss some modifications necessary in the degenerate case. The inverse and the realization problems are mentioned, too.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

55-76

Source:

Mathematica bohemica | 2000 Volume:125 | Number:1

Harvested from:

CDK

Metadata only:

false