Stellar Orbital Studies in Normal Spiral Galaxies I: Restrictions to the
  Pitch Angle
  We built a family of non-axisymmetric potential models for normal non-barred
or weakly-barred spiral galaxies as defined in the simplest classification of
galaxies: the Hubble sequence. For this purpose a three-dimensional
self-gravitating model for spiral arms PERLAS is superimposed to the galactic
axisymmetric potentials. We analyze the stellar dynamics varying only the pitch
angle of the spiral arms, from 4$\deg$ to 40$\deg$, for an Sa galaxy, from
8$\deg$ to 45$\deg$, for an Sb galaxy, and from 10$\deg$ to 60$\deg$, for an Sc
galaxy. Self-consistency is indirectly tested through periodic orbital
analysis, and through density response studies for each morphological type.
Based on ordered behavior, periodic orbits studies show that for pitch angles
up to approximately $15\deg$, $18\deg$, and $20\deg$ for Sa, Sb and Sc
galaxies, respectively, the density response supports the spiral arms
potential, a requisite for the existence of a long-lasting large-scale spiral
structure. Beyond those limits, the density response tends to "avoid" the
potential imposed by mantaining lower pitch angles in the density response; in
that case the spiral arms may be explained as transient features rather than
long-lasting large-scale structures. In a second limit, from a phase space
orbital study based on chaotic behavior, we found that for pitch angles larger
than $\sim30\deg$, $\sim40\deg$ and $\sim50\deg$ for Sa, Sb, and Sc galaxies,
respectively, chaotic orbits dominate all phase space prograde region that
surrounds the periodic orbits sculpting the spiral arms and even destroying
them. This result seems to be in good agreement with observations of pitch
angles in typical isolated normal spiral galaxies.
