  With the aim of studying the nonlinear stellar and gaseous response to the
gravitational potential of a galaxy such as the Milky Way, we have modeled 3D
galactic spiral arms as a superposition of inhomogeneous oblate spheroids and
added their contribution to an axisymmetric model of the Galactic mass
distribution. Three spiral loci are proposed here, based in different sets of
observations. A comparison of our model with a tight-winding approximation
shows that the self-gravitation of the whole spiral pattern is important in the
middle and outer galactic regions. As a first step to full 3D calculations the
model is suitable for, we have explored the stellar orbital structure in the
midplane of the Galaxy. We present the standard analysis in the pattern
rotating frame, and complement this analysis with orbital information from the
Galactic inertial frame. Prograde and retrograde orbits are defined
unambiguously in the inertial frame, then labeled as such in the Poincar\'e
diagrams of the non-inertial frame. In this manner we found a sharp separatrix
between the two classes of orbits. Chaos is restricted to the prograde orbits,
and its onset occurs for the higher spiral perturbation considered plausible in
our Galaxy.
