Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model
arXiv:nlin/0101033 · doi:10.1134/1.1490107
Abstract
Relations between the free motion on the GL^+(n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with the pairwise 1/sinh^2 x ``potential'' (Euler-Calogero-Sutherland model) is discussed in the framework of Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: due to the continuous invariance and due to the discrete symmetry. It is shown that after projection on the corresponding invariant manifolds the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases.
11 pages, ReVTeX, no figures. Based on talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. V2: The Lax representation and typos corrected, two references added