Chaotic motion around prolate deformed bodies

The motion of particles in the field of forces associated to an axially symmetric attraction center modeled by a monopolar term plus a prolate quadrupole deformations is studied using Poincaré surface of sections and Lyapunov characteristic numbers. We find chaotic motion for certain values of the parameters, and that the instability of the orbits increases when the quadrupole parameter increases. A general relativistic analog is briefly discussed.