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)
Yuri N FEDOROV
Yuri N FEDOROV
Available Online 1 December 2005.
- https://doi.org/10.2991/jnmp.2005.12.s2.7How to use a DOI?
- 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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Cite this article
TY - JOUR AU - Yuri N FEDOROV PY - 2005 DA - 2005/12 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 - https://doi.org/10.2991/jnmp.2005.12.s2.7 ID - FEDOROV2005 ER -