  The concept of Space Manifold Dynamics is a new method of space research. We
have applied it along with the basic idea of the method of Ott, Grebogi and
York (OGY method) to stabilize the motion of a spacecraft around the triangular
Lagrange point L5 of the Earth--Moon system. We have determined the escape rate
of the trajectories in the general three- and four-body problem and estimated
the average lifetime of the particles. Integrating the two models we mapped in
detail the phase space around the L5 point of the Earth--Moon system. Using the
phase space portrait our next goal was to apply a modified OGY method to keep a
spacecraft close to the vicinity of L5. We modified the equation of motions
with the addition of a time dependent force to the motion of the spacecraft. In
our orbit--keeping procedure there are three free parameters: (i) the magnitude
of the thrust, (ii) the start time and (iii) the length of the control. Based
on our numerical experiments we were able to determine possible values for
these parameters and successfully apply a control phase to a spacecraft to keep
it on orbit around L5.
