### 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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