Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2005-05-18
J. Nonl. Math. Phys. 12 (2005), 77-94
Nonlinear Sciences
Exactly Solvable and Integrable Systems
18 pages, 1 Figure
Scientific paper
We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety $\bar{\cal V}(k,m)$, and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic map $\cal B$ on the 4-dimensional variety ${\cal V}(2,3)$. 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 $\cal B$ to $so^*(3)$ gives a new explicit discretization of the Euler top in the angular momentum space, which preserves first integrals of the continuous system.
No associations
LandOfFree
Integrable flows and Backlund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Integrable flows and Backlund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable flows and Backlund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-710387