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arXiv · nlin/0101033

Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model

A. M. Khvedelidze·D. M. Mladenov
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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.

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A. M. Khvedelidze, D. M. Mladenov. 2001-01-30. Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model. https://doi.org/10.1134/1.1490107

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