We study the separability of the Neumann–Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1, 1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.
A geometric approach to the separability of the Neumann-Rosochatius system
BARTOCCI, CLAUDIO;
2004-01-01
Abstract
We study the separability of the Neumann–Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1, 1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.
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