  The Relationship between the Neumann system and the Jacobi system in
arbitrary dimensions is elucidated from the point of view of constrained
Hamiltonian systems. Dirac brackets for canonical variables of both systems are
derived from the constrained Hamiltonians. The geodesic equations corresponding
to the Rosochatius system are studied as an application of our method. As a
consequence a new class of nonlinear integrable equations is derived along with
their conserved quantities.
