  We study the transition from regular to chaotic motion in a prolate
elliptical galaxy dynamical model with a bulge and a dense nucleus. Our
numerical investigation shows that stars with angular momentum Lz less than or
equal to a critical value Lzc, moving near the galactic plane, are scattered to
higher z, when reaching the central region of the galaxy, thus displaying
chaotic motion. An inverse square law relationship was found to exist between
the radius of the bulge and the critical value Lzc of the angular momentum. On
the other hand, a linear relationship exists between the mass of the nucleus
and Lzc. The numerically obtained results are explained using theoretical
arguments. Our study shows that there are connections between regular or
chaotic motion and the physical parameters of the system, such as the star's
angular momentum and mass, the scale length of the nucleus and the radius of
the bulge. The results are compared with the outcomes of previous work.
