Integrable flows and Bäcklund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)
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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.
- © 2006, the Authors. Published by Atlantis Press.
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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 -