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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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard McGehee
Richard Paul McGehee (born 20 September 1943, in San Diego) is an American mathematician, who works on dynamical systems with special emphasis on celestial mechanics. McGehee received from Caltech in 1964 his bachelor's degree and from University of Wisconsin–Madison in 1965 his master's degree and in 1969 his Ph.D. under Charles C. Conley with thesis ''Homoclinic orbits in the restricted three body problem''. As a postdoc he was at the Courant Institute of Mathematical Sciences of New York University. In 1970 he became an assistant professor and in 1979 a full professor at the University of Minnesota in Minneapolis, where he was from 1994 to 1998 the director of the Center for the Computation and Visualization of Geometric Structures. In the 1970s he introduced a coordinate transformation (now known as the McGehee transformation) which he used to regularize singularities arising in the Newtonian three-body problem. In 1975 he, with John N. Mather, proved that for the Newtonian c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |