  The dynamics of extended bodies endowed with multipolar structure up to the
mass quadrupole moment is investigated in the Schwarzschild background
according to the Dixon's model, extending previous works. The whole set of
evolution equations is numerically integrated under the simplifying assumptions
of constant frame components of the quadrupole tensor and that the motion of
the center of mass be confined on the equatorial plane, the spin vector being
orthogonal to it. The equations of motion are also solved analytically in the
limit of small values of the characteristic length scales associated with the
spin and quadrupole with respect to the background curvature characteristic
length. The results are qualitatively and quantitatively different from
previous analyses involving only spin structures. In particular, the presence
of the quadrupole turns out to be responsible for the onset of a non-zero spin
angular momentum, even if initially absent.
