here some results for the 5-earth sim .
I ran them for about 400 years .
Timestep = 128 sec .
Tilmestep was perhaps too big for the 4 inner planets , as they lost their moons . The 5th earth kept his moon .
Interesting is the following :
1. Time before the Kozai becomes "visible" rises about exponentially with AU ( see last Excel-graph ) . This means that the moons of the outer planets must be protected by "time" .
2. Inclination changes slowly in the beginning , but increases rapidly as the ecc. goes to 1.
3. After reaching the max ecc the system gets in a cycle with decreasing ecc and decreasing incl , rising again , a.s.o.
It is further interesting to run the sim with a smaller time step in order to obtain the frequency of the fluctations of incl . ( avoiding the moons are lost ) .
I tried to correlate the frequency of oscillation tothe time needed to obtain full ecc , but data are to few . Such a link must exist surely .
Note : running the sim I observed that the moon of the first earth changed the orientation at ecc=1 , meaning she returned to the earth in the some direction as she come from , meaning rotating clockwise instead of anti-clockwise .
Really surprising !!!
** modified by Tony -- added img tags.