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So, in Naoz et al. (2013) is described the Kozai mechanism on three-body systems. I've tried to solve the equations (B1) - (B17) for the example described in the Figure 3 and I got something like this:

enter image description here

enter image description here

Note that I got the exact same result until $\sim$ 33 Myr (black arrow), then the cycles change radically. Is this usual?. Do Kodai cycles tend to change over time like this or they actually remain with the same "shape" as time goes by? If the latter, isn't a way to predict the behavior of Kodai cycles as t tends to infinity?

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  • $\begingroup$ The link isn't working for me. I get a timeout error. The change of behaviour at 33Myr could suggest some kind of overflow error. $\endgroup$ – James K Mar 20 at 21:45
  • $\begingroup$ Now the link is fixed. $\endgroup$ – Carlos Vázquez Monzón Mar 20 at 21:49
  • $\begingroup$ Wait, Figure 3 ends at 25 Myr, so you did not get "the exact same result until ~33 Myr". Perhaps they cut it off at 25 for just this reason? $\endgroup$ – uhoh Mar 21 at 2:13
  • $\begingroup$ If you want to explore any possible numerical errors you can also ask about that in Scientific Computing SE. I've had excellent luck receiving great answers there, see for example this and this. The first one reminds me; did you use a symplectic integrator? Have you tried adjusting any optional step size and/or precision or accuracy requirements specified to the integration routine to see what effect it has? What integrator did you use? $\endgroup$ – uhoh Mar 21 at 2:15
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    $\begingroup$ I use a Mathematica package call TIDES. I don't think there's a mistake, nor in the step size(I chose 5*10^6 points), but I may check out for mistakes. The thing is, do Kozai cycles maintain over time or can change like that? If they maintain is clearly a numerical error... $\endgroup$ – Carlos Vázquez Monzón Mar 21 at 2:31

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