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
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually ...
where the collision occurs into a collision
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
, 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.
References
*Celestial Encounters, The Origins of Chaos and Stability, Diacu/Holmes, {{ISBN, 0-691-00545-1, Princeton Science Library
Classical mechanics