Matrix G-strands

Authors

Darryl Holm, Imperial College London
Rossen Ivanov, Technological University DublinFollow

Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics

Publication Details

Nonlinearity 27 (2014) 1445–1469; doi:10.1088/0951-7715/27/6/1445

Abstract

We discuss three examples in which one may extend integrable Euler–Poincare ordinary differential equations to integrable Euler–Poincare partial differential
equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained in examples in the language of vectors in R³.

DOI

http://doi.org10.1088/0951-7715/27/6/1445

Recommended Citation

Holm, D. and Ivanov, R. Matrix G-Strands, Nonlinearity 27 (2014) 1445–1469; doi:10.1088/0951-7715/27/6/1445

Funder

ERC