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Lie transform

(Lie transformation)
(type of infinitesimal transform)

A Lie transform or Lie transformation is a specific type of infinitesimal transform/transformation (arbitrarily small transformations) of manifolds that form a type of transformation group termed a Lie group, which has an associated algebra (Lie algebra). An application for them is the development of perturbation theories using them, using abstract algebra concepts and methods to handle the differential equations of Hamiltonian mechanical systems. This is used for analysis of orbits in celestial mechanics as well as in electron orbits.

Lie transforms, groups and algebras began with the work of mathematician Sophus Lie.


(mathematics,differential equations,celestial mechanics,orbits)
http://en.wikipedia.org/wiki/Infinitesimal_transformation

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