  We present a numerical investigation of the dynamics of one falling oblate
ellipsoid particle in a viscous fluid, in three dimensions, using a
constrained-force technique \cite{Kai}, \cite{Kaih} and \cite{Esa}. We study
the dynamical behavior of the oblate for a typical downward motion and obtain
the trajectory, velocity, and orientation of the particle. We analyze the
dynamics of the oblate generated when the height of the container, the
aspect-ratio, and the dynamical viscosity are changed. Three types of falling
motions are established: steady-falling, periodic oscillations and chaotic
oscillations. In the periodic regime we find a behavior similar to the case of
falling flat strips reported in ref. \cite{Belmonte}. In the chaotic regime the
trajectory of the oblate is characterized by a high sensitivity to tiny
variations in the initial orientation. The Lyapunov exponent is $\lambda =
0.052 \pm 0.005$. A phase space comparing to the results of ref \cite{Nori}, is
shown.
