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1D three-body problem (with spherical shell)

  1. Aug 11, 2010 #1
    Let's suppose that we have two point particles with masses m1,m2 and the spherical shell with mass M, placed in a line, at distances h1,h2 and H from 0 in that line (0 is the center of some inertial frame of reference). The initial conditions and the equations of motion are the following:



    [itex]h_1'(0)=h_2'(0)=H'(0)=0[/itex] (time derivative)

    (the mass m1 is in the center of the spherical shell)




    Is there any way to solve this problem (to find the positions of the masses as functions ot the time)?
  2. jcsd
  3. Aug 11, 2010 #2


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    Gold Member

    integrate twice with respect to t?

    Or are H and h actually arbitrary functions of t?
  4. Aug 11, 2010 #3
    Yes they are functions of t, i think, so it's more complicated.

    Edit: I'm going to create the same thread in Classical Physics section so the moderators can close this one. Thnx!
    Last edited: Aug 11, 2010
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