  Following Papadakis (2005)'s numerical exploration of the Chermnykh's
problem, we here study a Chermnykh-like problem motivated by the astrophysical
applications. We find that both the equilibrium points and solution curves
become quite different from the ones of the classical planar restricted
three-body problem. In addition to the usual Lagrangian points, there are new
equilibrium points in our system. We also calculate the Lyapunov Exponents for
some example orbits. We conclude that it seems there are more chaotic orbits
for the system when there is a belt to interact with.
