Examples from the calculus of variations III. Legendre and Jacobi conditions.

Title:

Examples from the calculus of variations III. Legendre and Jacobi conditions.

Creator:

Chrastina, Jan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ce2f770d-1b03-437f-a5dc-01bc57863aa4
uuid:ce2f770d-1b03-437f-a5dc-01bc57863aa4
doi:10.21136/MB.2001.133926

Subject:

Legendre condition, Jacobi condition, Poincaré-Cartan form, Lagrange problem, and degenerate variational integral

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.

Language:

English

Rights:

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

Coverage:

93-111

Source:

Mathematica bohemica | 2001 Volume:126 | Number:1

Harvested from:

CDK

Metadata only:

false