We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these 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. In these simulations 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 owing 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 that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform 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.
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