Recently were discovered rings of particles orbiting small bodies in outer solar system (Chariklo and Haumea). Due to the size of such bodies they are expected to have a non-spherical shape. At least one of them (Haumea) is known to have
a strong ellipsoidal format. In the present work we study the orbital evolution of particles in a gravitational potential of ellipsoidal shape, including the J2 and C22 gravitational components.
We performed a study on the contribution of each component. The results show that the use of the classical geometric orbital elements are not fully adequate to deal with such dynamics. So, we propose some correction on that.
The dynamical structure of the space around ellipsoidal bodies were also explored through the Poincaré surface of section technique, where stable (resonant or not) and unstable regions were identified.