Quote from Tony   on 10/28/06 at 18:59:57:

 
EDIT: I managed to restart the simulation using the final values from the saved output file from the crashed sim. I'll use the Mean Anomalies that I started with - hopefully that won't make too much of a difference. I should be able to add the output to the existing text file.  
 
I guess the resume.gsim didn't save because the program wasn't closed down manually - since it crashed, all it had to go on were the initial parameters.

oops, I missed your "crash post".  Tough way to learn to autosave.  Hmmm, I could make Gravity Simulator create a backup sim every few minutes like Microsoft Word does:  "backup.gsim".
 
I'm glad you could reconstrut it.  I doubt that the anomolies will affect your results since nothing is locked into resonance.

Got a reply from Genya Takeda which was rather interesting. Apparently the inclination is also supposed to oscilate between the starting relative inclination and that critical value of about 40 degrees! This isn't happening in the GravSim simulation - the relative inclination is already well below the critical value. So something is still not right here in GravSim- either the algorithm used here isn't accurate enough or the timestep is still too large. More experiments are due, I guess!
 
However, he also mentioned that the Arg of Peri is either going to be circling around 360° or it's going to be oscillating around 90°, and it does look like this might be happening here! Remember, the sim did vary wildly around 360° at first, and now it looks like it's partway through a long period oscillation around 90°...

Quote from Tony   on 10/28/06 at 22:38:24:

 
Erm, wait a minute... the ecliptic can be anything you want if there's two bodies orbiting the star. You can set the planet at 0 degrees inclination and the companion at 75, and the planet's orbit will be the ecliptic. Or you can set the companion's orbit at 0 degrees and the planet's at 75 and the companion's orbit will be the ecliptic. It only gets fixed if you have a several bodies orbiting in roughly the same plane and one or two well outside it - in which case the plane that most of the bodies orbits in is the ecliptic. (technically, the Ecliptic in the solar system is the plane of Earth's orbit around the sun, but the other seven planets orbit roughly in that plane)
 
Of course the difference in orientation of the orbits is probably a problem, because I guess then you're talking about dog-leg angles when calculating the difference in inclinations. That I could understand being a problem.
 
Unless I've completely missed the point of what you're saying .

Hi Mal , inclination will grow rapîdly as e wil go to 1 .  
I have the same experience with the 5-earths sim .  
I'll try to upload the images .  

Quote from frankuitaalst   on 10/29/06 at 01:27:36:

 
Hm, that shouldn't be happening - the relative inclination is supposed to be going between the starting value and 40 degrees.

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.

In order to "save" the moons I started the sim with reduced timestep ( 32 instead of 128) . I lost already 3 moons ( also for 2Au , the one with the double peaks ) . I wonder how the results will be ... Keep you informed .  
BTW : the integration is done by Runge Kutta 4 or another method ?  
Frank