title: McGehee transformation
text: # McGehee transformation
  
  The McGehee transformation was introduced by Richard McGehee to study the triple collision singularity in the n-body problem.
  
  The transformation blows up the single point in phase space where the collision occurs into a collision manifold, the phase space point is cut out and in its place a smooth manifold is pasted. This allows the phase space singularity to be studied in detail.
  
  What McGehee found was a distorted sphere with four horns pulled out to infinity and the points at their tips deleted. McGehee then went on to study the flow on the collision manifold.
  
  