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

Dynamics of quadrupolar bodies in a Schwarzschild spacetime