Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 2, December 2005, Pages 77 - 94

Integrable flows and Bäcklund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)

Authors
Yuri N. Fedorov
Corresponding Author
Yuri N. Fedorov
Available Online 1 December 2005.
DOI
10.2991/jnmp.2005.12.s2.7How to use a DOI?
Abstract

We show that the m-dimensional Euler­Manakov top on so (m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety ¯V(k, m), and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic map B on the dimensional variety V(2, 3). The map admits two different reductions, namely, to the Lie group SO(3) and to the coalgebra so (3). The first reduction provides a discretization of the motion of the classical Euler top in space and has a transparent geometric interpretation, which can be regarded as a discrete version of the celebrated Poinsot model of motion and which inherits some properties of another discrete system, the elliptic billiard. The reduction of B to so (3) gives a new explicit discretization of the Eler top in the angular momentum space, which preserves first integrals of the continuous system.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - Supplement 2
Pages
77 - 94
Publication Date
2005/12/01
ISBN
91-974824-5-5
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2005.12.s2.7How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Yuri N. Fedorov
PY  - 2005
DA  - 2005/12/01
TI  - Integrable flows and Bäcklund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)
JO  - Journal of Nonlinear Mathematical Physics
SP  - 77
EP  - 94
VL  - 12
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.7
DO  - 10.2991/jnmp.2005.12.s2.7
ID  - Fedorov2005
ER  -