### Perturbation Theory

(breaking an equation into a solvable part and approximatable part)

**Perturbation Theory** is a generalization of
a mechanism for orbiting three body problems,
by breaking it into two simple two-body orbiting problems
along with an unsolvable but approximatable "perturbation"
of the two orbits. As a theory, it has been generalized
to handle other unsolvable equations (often differential
equations) of other kinds of physical systems,
in chemistry, Quantum Mechanics, etc.
The perturbation is cast as a series of ever-smaller
solvable equations, e.g., like a Taylor Series.

A **First Order Perturbation Problem**
(or **Regular Perturbation Problem**)
is a problem that includes a very small parameter and
the solution can be found by approximating that parameter as zero.
If such an approximation is too far off,
it is known as a **Second Order Perturbation Problem**
(or **Singular Perturbation Problem** or **Degenerate Perturbation Problem**).

The Hamiltonian is useful in Perturbation Theory to study Secular
(long term) motions related to planetary orbits, and is useful
in series-expanded form to provide tractable estimations
and because it can handle coordinate transformations that simplify
solutions, sometimes effectively eliminating a coordinate. With a
Multipole Expansion, terms through the **Octupole Term**
can be necessary to explain observed exotic Extra-Solar Planet orbits.

(*orbits,dynamics,mathematics*)
http://en.wikipedia.org/wiki/Perturbation_theory

**Referenced by:**

N-Body Problem

Zel'dovich Approximation

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