  We examine a large random sample of orbits in self-consistent simulations of
N-body bars. Orbits in the bars are classified both visually and with a new
automated orbit classification method based on frequency analysis. The well
known prograde x1 orbit family originates from the same parent orbit as the box
orbits in stationary and rotating triaxial ellipsoids. However only a small
fraction of bar orbits ~4% have predominately prograde motion like their
periodic parent orbit. Most bar orbits arising from the x1 orbit have little
net angular momentum in the bar frame making them equivalent to box orbits in
rotating triaxial potentials. A small fraction of bar orbits (~7%) are long
axis tubes that behave exactly like those in triaxial ellipsoids:they are
tipped about the intermediate-axis due to the Coriolis force, with the sense of
tipping determined by the sign of their angular momentum about the long axis.
No orbits parented by prograde periodic x2 orbits are found in the pure bar
model, but a tiny population (~2%) of short axis tube orbits parented by
retrograde x4 orbits are found. When a central point mass representing a
supermassive black hole (SMBH) is grown adiabatically at the center of the bar,
those orbits that lie in the immediate vicinity of the SMBH are transformed
into precessing Keplerian orbits (PKOs) which belong the same major families
(short axis tubes, long axis tubes and boxes) occupying the bar at larger
radii. During the growth of a SMBH the inflow of mass and outward transport of
angular momentum transforms some x1 and long axis tube orbits into prograde
short axis tubes. This study has important implications for future attempts to
constrain the masses of SMBHs in barred galaxies using orbit based methods like
the Schwarzschild orbit superposition scheme and for understanding the observed
features in barred galaxies.
