General Jacobi coordinates and Herman resonance for some nonheliocentric celestial \(N\)-body problems (Q1987316)

The paper implements a combinatorial algorithm, based on full binary trees, to construct general Jacobi coordinates for the \(N\)-body problem with arbitrary positive masses. The resulting Hamiltonian consists of a nonheliocentric part of \(N-1\) independent Keplerian motions and a perturbation term. The combinatorial algorithm, based on the caterpillar binary tree, is specifically applied to the \(5\)-body problem with arbitrary positive masses, giving the main result of the paper. This gives a Hamiltonian for the \(5\)-body problem which approximates the motion as that of \(4\) nonheliocentric independent Keplerian motions plus a perturbation term. Averaging is applied to this Hamiltonian followed by linearization at the origin to establish Herman resonance.