  Starting from a continuum constituted by charged tops, we formulate the
classical counterpart of a previously obtained covariant continuity-like
equation for the spin current. Such a formulism provides an intuitive picture
to elucidate the non-conservation of the spin current and to interpret the
condition for the emergence of an infinite spin relaxation time. It also
facilitates the discussion on the spin precession in a one-dimensional quantum
wire with Dresselhaus and Rashba spin-orbit couplings. Furthermore, we derive
the diffusion equations for both the charge and spin densities and find that
they couple to each other due to the Zitterbewegung.
