  We consider two types of mechanical coupling between the crust and the core
of a precessing neutron star. First, we find that a hydromagnetic (MHD)
coupling between the crust and the core strongly modifies the star's
precessional modes when $t_a\le\sim (T_s\times T_p)^{1/2}$; here $t_a$ is the
Alfven crossing timescale, and $T_s$ and $T_p$ are the star's spin and
precession periods, respectively. We argue that in a precessing pulsar PSR
B1828-11 the restoring MHD stress prevents a free wobble of the crust relative
to the non-precessing core. Instead, the crust and the proton-electron plasma
in the core must precess in unison, and their combined ellipticity determines
the period of precession. Link has recently shown that the neutron superfluid
vortices in the core of PSR B1828-11 cannot be pinned to the plasma; he has
also argued that this lack of pinning is expected if the proton Fermi liquid in
the core is type-I superconductor. In this case, the neutron superfluid is
dynamically decoupled from the precessing motion. The pulsar's precession
decays due to the mutual friction between the neutron superfluid and the plasma
in the core. The decay is expected to occur over tens to hundreds of precession
periods and may be measurable over a human lifetime. Such a measurement would
provide information about the strong n-p interaction in the neutron-star core.
Second, we consider the effect of gravitomagnetic coupling between the neutron
superfluid in the core and the rest of the star and show that this coupling
changes the rate of precession by about 10%. The general formalism developed in
this paper may be useful for other applications.
