In an effort to understand better the formation and evolution of barred gal
axies, we have examined the properties of equatorial orbits in the effectiv
e potential of one specific model of a rapidly rotating, steady state gasdy
namical bar that has been constructed via a self-consistent hydrodynamical
simulation. At a given value of the Jacobi constant, roughly half of all te
st particles (stars) that are injected into the equatorial plane of this po
tential follow quasi-ergodic orbits; most regular prograde orbits have an o
verall "bow tie" shape; and some trace out trajectories that resemble the x
(4) family of regular, retrograde orbits. The bow tie orbits appear to be r
elated to the 4/1 orbit family discussed by Contopoulous in 1988, but parti
cles moving along a bow tie orbit pass very close to the center of the bar
twice each orbit. Unlike the barlike configurations that previously have be
en constructed using dissipationless, N-body simulation techniques, the eff
ective potential of our gasdynamical bar is very shallow and generally does
not support the x(1) family of orbits. If primordial galaxies evolve to a
rapidly rotating barlike configuration before a significant amount of star
formation has taken place and then stars form from the gas that makes up th
e bar, the initial stellar distribution function should consist of orbits t
hat are (1) supported by the gaseous barlike potential and (2) restricted t
o have initial conditions dictated by the gasdynamics of the bar. With this
"restriction hypothesis" in mind, we propose that stellar dynamical system
s that form from gaseous bars will have characteristics that differ signifi
cantly from systems that form from a bisymmetric instability in an initiall
y axisymmetric stellar system. Since bow tie orbits are preferred over x(1)
orbits, for example, such systems should have a more boxy or peanut shape
when seen face-on; there will be a mechanism for funneling material more di
rectly into the center of the galaxy; and, near the galaxy center, stars ma
y appear to move along retrograde trajectories.