  The magnetic levitation forces of a superconducting disk (SC) levitated by a
cylindrical permanent magnet (PM) have been calculated from first principles
for superconductors with finite thickness. The current $j(\rho,z)$ and field
$B(\rho,z)$ profiles in the SC in the non-uniform magnetic field generated by
the PM have been derived. The levitation force is observed to depend
non-linearly on the critical current density $j_c$ and on the thickness of the
SC. The flux creep is described by a current-voltage law $E(j)=E_c(j/j_c)^n$,
from which we show that the levitation force depends on the speed at which the
PM approaches or recedes from the SC, which accounts for the experimentally
observed force creep phenomenon. The stiffness of the system has been derived
by calculating the minor force loops. The numerical results reproduce many of
the features exhibited by experiments.
