Chaos in a gravitational field with dipoles

In this paper we investigate the dynamics of a test particle in the gravitational field with dipoles. At first we study the gravitational potential by numerical simulations, we find that, for appropriate parameters, there are two different cases in the potential curve: one is the one-well case with a stable critical point, and the other is the three-well case with three stable critical points and two unstable critical points. By performing Poincaré sections for different values of the parameters and initial conditions, we find a regular motion and a chaotic motion. From these Poincaré sections, we further confirm that the chaotic motion of the test particle originates mainly from the dipoles.