  We present the exact solutions of the homoclinic orbits for the timelike
geodesics of the particle on the general nonequatorial orbits in the
Kerr-Newman black holes. The homoclinic orbit is the separatrix between bound
and plunging geodesics, a solution that asymptotes to an energetically bound,
unstable spherical orbit. The solutions are written in terms of the elliptical
integrals and the Jacobi elliptic functions of manifestly real functions of the
Mino time where we focus on the effect from the charge of the black hole to the
homoclinic orbits. The parameter space of the homoclinic solutions is explored.
The nonequatorial homoclinic orbits in Kerr cases can be obtained by setting
the charge of the black holes to be zero. The homoclinic orbits and the
associated phase portrait as a function of the radial position and its
derivation with respect to the Mino time are plotted using the analytical
solutions. In particular, the solutions can reduce to the zero azimuthal
angular moment homoclinic orbits for understanding the frame dragging effects
from the spin as well as the charge of the black hole. The implications of the
obtained results to observations are discussed.
