We design an efficient orbital integration scheme for the general N-body problem that preserves all the conserved quantities except the angular momentum. This scheme is based on the chain concept and is regarded as an extension of a d'Alembert-type scheme for constrained Hamiltonian systems. It also coincides with the discrete-time general three-body problem for particle number N = 3. Although the proposed scheme is only second-order accurate, it can accurately reproduce some periodic orbits, which cannot be done with generic geometric numerical integrators.
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