Astrophysics (Index)About

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). They can be used in the development of perturbation theories, 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, Lie groups and Lie algebras are based on underlying work by the mathematician Sophus Lie and named for him.


(mathematics,differential equations,celestial mechanics,orbits)
Further reading:
http://en.wikipedia.org/wiki/Infinitesimal_transformation
http://en.wikipedia.org/wiki/Lie_group
http://en.wikipedia.org/wiki/Lie_algebra
http://en.wikipedia.org/wiki/Lie_theory
https://pages.uoregon.edu/arkadiy/howe.very.basic.lie.theory.pdf
https://arxiv.org/abs/1104.1106

Index