As it will be briefly discussed below, the only singularities in the 3-body problem are binary collisions ( collisions between two particles at an instant ), and triple collisions ( collisions between three particles at an instant ).
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The question intrigued me becaus ( again, if i recollect correctly ) a classical triple collision is mathematically singular, that is, if three classical bodies were to collide at exactly the same time there is no way to determine the resulting trajectories.
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