Jacobi coordinates

In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation.

These coordinates are particularly common in treating polyatomic molecules and chemical reactions,[3] and in celestial mechanics.

[4] An algorithm for generating the Jacobi coordinates for N bodies may be based upon binary trees.

The position coordinates xj and xk are replaced by their relative position rjk = xj − xk and by the vector to their center of mass Rjk = (mj qj + mkqk)/(mj + mk).

The order of children indicates the relative coordinate points from xk to xj.

If one is interested in evaluating a free energy operator in these coordinates, one obtains In the calculations can be useful the following identity

Jacobi coordinates for two-body problem ; Jacobi coordinates are and with . [ 1 ]
A possible set of Jacobi coordinates for four-body problem; the Jacobi coordinates are r 1 , r 2 , r 3 and the center of mass R . See Cornille. [ 2 ]