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

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.

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title:		Integrable flows and Bäcklund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)
publication:		JNMP
volume-issue:		12 - Supplement 2
pages:		77 - 94
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.s2.7 (how to use a DOI)
author(s):		Yuri N FEDOROV
publication date:		December 2005
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:		© Atlantis Press. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		12s2_07n.pdf (242 K)