  In this paper we study the Neumann system, which describes the harmonic
oscillator (of arbitrary dimension) constrained to the sphere. In particular we
will consider the confluent case where two eigenvalues of the potential
coincide, which implies that the system has S^{1} symmetry. We will prove
complete algebraic integrability of confluent Neumann system and show that its
flow can be linearized on the generalized Jacobian torus of some singular
algebraic curve. The symplectic reduction of S^{1} action will be described and
we will show that the general Rosochatius system is a symplectic quotient of
the confluent Neumann system, where all the eigenvalues of the potential are
double. This will give a new mechanical interpretation of the Rosochatius
system.
