Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Title:

Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Creator:

Brajerčík, Ján

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7253eda7-0c2a-4884-af87-5f2bcf7b4f6e
uuid:7253eda7-0c2a-4884-af87-5f2bcf7b4f6e

Subject:

Frame bundle, Euler-Lagrange equations, invariant Lagrangian, and Euler-Poincaré reduction

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\mu \colon FX \to X$ be a principal bundle of frames with the structure group ${\rm Gl}_{n}(\mathbb R)$. It is shown that the variational problem, defined by ${\rm Gl}_{n}(\mathbb R)$-invariant Lagrangian on $J^{r} FX$, can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

Language:

English

Rights:

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

Coverage:

1063-1076

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:4

Harvested from:

CDK

Metadata only:

false