  The motion of a point mass in the J2 problem has been generalized to that of
a rigid body in a J2 gravity field for new high-precision applications in the
celestial mechanics and astrodynamics. Unlike the original J2 problem, the
gravitational orbit-rotation coupling of the rigid body is considered in the
generalized problem. The existence and properties of both the classical and
non-classical relative equilibria of the rigid body are investigated in more
details in the present paper based on our previous results. We
nondimensionalize the system by the characteristic time and length to make the
study more general. Through the study, it is found that the classical relative
equilibria can always exist in the real physical situation. Numerical results
suggest that the non-classical relative equilibria only can exist in the case
of a negative J2, i.e., the central body is elongated; they cannot exist in the
case of a positive J2 when the central body is oblate. In the case of a
negative J2, the effect of the orbit-rotation coupling of the rigid body on the
existence of the non-classical relative equilibria can be positive or negative,
which depends on the values of J2 and the angular velocity. The bifurcation
from the classical relative equilibria, at which the non-classical relative
equilibria appear, has been shown with different parameters of the system. Our
results here have given more details of the relative equilibria than our
previous paper, in which the existence conditions of the relative equilibria
are derived and primarily studied. Our results have also extended the previous
results on the relative equilibria of a rigid body in a central gravity field
by taking into account the oblateness of the central body.
