d'Alembert-type scheme with a chain regularization for N-body problem

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We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an extension of a d'Alembert-type scheme (Betsch 2005) for constrained Hamiltonian systems. It also coincides with the discrete-time general three-body problem (Minesaki 2013) for particle number N = 3. Although the proposed scheme is only second-order accurate, it can accurately reproduce some periodic orbits, which generic geometric numerical integrators cannot do.