A new dynamical model for the study of galactic structure

In the present article, we present a new gravitational galactic model, describing motion in elliptical as well as in disk galaxies, by suitably choosing the dynamical parameters. Moreover, a new dynamical parameter, the S(g) spectrum, is introduced and used, in order to detect islandic motion of resonant orbits and the evolution of the sticky regions. We investigate the regular or chaotic character of motion, with emphasis in the different dynamical models and make an extensive study of the sticky regions of the system. We use the classical method of the Poincaré r ? p_r phase plane and the new dynamical parameter of the S(g) spectrum. The L.C.E is used, in order to make an estimation of the degree of chaos in our galactic model. In both cases, the numerical calculations, suggest that our new model, displays a wide variety of families of regular orbits, compared to other galactic models. In addition to the regular motion, this new model displays also chaotic regions. Furthermore, the extent of the chaotic regions increases, as the value of the flatness parameter b of the model increases. Moreover, our simulations indicate, that the degree of chaos in elliptical galaxies, is much smaller than that in dense disk galaxies. In both cases numerical calculations show, that the degree of chaos increases linearly, as the flatness parameter b increases. In addition, a linear relationship between the critical value of angular momentum and the b parameter if found, in both cases (elliptical and disk galaxies). Some theoretical arguments to support the numerical outcomes are presented. Comparison with earlier work is also made.