  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 $z = p_z
= 0$ using the Poincar\'e map as a basic tool and then we study the full 3
dimensional case using the SALI 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.
