  We study the dynamics of a dipolar Bose-Einstein condensate, like for example
a $^{52}$Cr or $^{164}$Dy condensate, interacting with a superconducting
surface. The magnetic dipole moments of the atoms in the Bose-Einstein
condensate induce eddy currents in the superconductor. The magnetic field
generated by eddy currents modifies the trapping potential such that the
center-of-mass oscillation frequency is shifted. We numerically solve the
Gross-Pitaevskii equation for this system and compare the results with
analytical approximations. We present an approximation that gives excellent
agreement with the numerical results. The eddy currents give rise to anharmonic
terms, which leads to the excitation of shape fluctuations of the condensate.
We discuss how the strength of the excitation of such modes can be increased by
exploiting resonances, and we examine the strength of the resonances as a
function of the center-of-mass oscillation amplitude of the condensate.
Finally, we study different orientations of the magnetic dipoles and discuss
favorable conditions for the experimental observation of the eddy current
effect.
