The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar, we introduce a new simple dynamical model and we explore the influence on the character of orbits of all the involved parameters of it, such as the mass and the scale length of the bar, the major semi-axis and the angular velocity of the bar, as well as the energy. Regions of phase space with ordered and chaotic motion are identified in dependence on these parameters and for breaking the rotational symmetry. First, we study in detail the dynamics in the invariant plane z = pz = 0 using the Poincaré map as a basic tool and then study the full three-dimensional case using the Smaller Alignment index method as principal tool for distinguishing between order and chaos. We also present strong evidence obtained through the numerical simulations that our new bar model can realistically describe the formation and the evolution of the observed twin spiral structure in barred galaxies.
