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**Up:** NON-INTEGRABILITY
OF THE MOTION **Previous:** The
General Main Satellite

There are several questions of practical interest which could arise
in connection with the non-integrability, such as the size of the chaotic
zones (as it was established by Simó [8]
in the *J*_{2}-problem) and, in general, its relevance from
a practical point of view. Most of these questions are still open and the
answers do not seem to be trivial. Some considerations about the physical
meaning of the orbits required by Ziglin's method, as well as some numerical
simulations can be seen in [7], where it
is shown the appearance of chaos (hard or soft) for moderate values of
*J*_{22} in the neighbourhood of the 1:1 resonant orbit.