  The kinetic term of the $N$-body Hamiltonian system defined on the surface of
the sphere is non-separable. As a result, standard explicit symplectic
integrators are inapplicable. We exploit an underlying hierarchy in the
structure of the kinetic term to construct an explicit time-reversible
symplectic scheme of second order. We use iterative applications of the method
to construct a fourth order scheme and demonstrate its efficiency.
