  We discuss motions of extended bodies in Kerr spacetime by using
Mathisson-Papapetrou-Dixon equations. We firstly solve the conditions for
circular orbits, and calculate the orbital frequency shift due to the mass
quadrupoles. The results show that we need not consider the spin-induced
quadrupoles in extreme-mass-ratio inspirals for spatial gravitational wave
detectors. We quantitatively investigate the temporal variation of rotational
velocity of the extended body due to the coupling of quadrupole and background
gravitational field. For generic orbits, we numerically integrate the
Mathisson-Papapetrou-Dixon equations for evolving the motion of an extended
body orbiting a Kerr black hole. By comparing with the monopole-dipole
approximation, we reveal the influences of quadrupole moments of extended
bodies on the orbital motion and chaotic dynamics of extreme-mass-ratio
systems. We do not find any chaotic orbits for the extended bodies with
physical spins and spin-induced quadrupoles. Possible implications for
gravitational wave detection and pulsar timing observation are outlined.

General Relativity and Quantum Cosmology