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

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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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  -