Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
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
Included in
Mathematics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
Nonlinearity 27 (2014) 1445–1469; doi:10.1088/0951-7715/27/6/1445