What are Jacobi coordinates, and why are they useful?

[AxiomOfChoice]

What are "Jacobi coordinates," and why are they useful?

I am working on a quantum chemistry problem involving triatomic molecules. My advisor keeps talking about "Jacobi coordinates" and how they're a calculational convenience when it comes time to write out the Hamiltonian. Can someone describe them to me, and why they make life easier? I can't seem to find a good resource for this on the Web...

 

[Meir Achuz]

Jacobi coordinates are coordinates for three bodies of equal mass, using the cm of two of them. The coordinates I like to use are
R=(r1+r2+r3)/3
r=(r1-r2)/2
rho=(2/3)[r3-(r1+r2)/2].
The more common Jacobi coordinates divide by square roots to make equations more symmetric, but they get more complicated in practice.
If one of the bodies has a different mass, then masses have to enter.