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Determining "boundedness" of particles in an n body simulation

  1. Sep 11, 2014 #1
    is there a numerical method to determine whether two bodies will stay bounded forever in an n body simulation? i know if the energy of a particle orbitting the origin is negative, then it is bounded, where -∫(force)dr+(dr/dt)2/2=energy.
    but im curious about a genereral case, where there are more than 2 bodys, and even forces that are not inverse square proportional where i dont necessarily have a potential to subtract kinetic energy from, just the ability to numerically do the line integral of force
    ∫ [Fx,fy,fz]*[dx/dt,dy/dt,dz/dt] dt
  2. jcsd
  3. Sep 11, 2014 #2


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    Staff: Mentor

    As soon as you have more than two objects, that is not possible in general any more. Energy doesn't help - two objects can move to a closer orbit, giving energy to a third (escaping) object, so a total negative energy does not mean the objects have to stay together (but two of them will).

    You can simulate the system for a very long time, of course, but then numerical errors are problematic.

    For two objects: if you can write down a potential, then you can check if energy conservation allows a separation. Note that this is not sufficient - a 1/r^3-law with two objects for example has circular orbits, but also unstable trajectories leading either to a separation or a collision.
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