The gravitational N-body problem is conservative — total energy and angular momentum are preserved exactly. Real astrophysical systems lose energy through tidal dissipation, gas drag, gravitational radiation. Adding dissipation to N-body simulations is straightforward: subtract energy at each timestep. But naive energy removal also destroys angular momentum, producing orbits that spiral inward too fast and in the wrong plane.
Martínez et al. (arXiv:2603.12452) construct a dissipative model for the point-mass N-body problem that removes energy while preserving angular momentum exactly. The dissipative force on each body is tangential to its orbit — it slows the body without torquing it. The system decays toward lower energy configurations while maintaining the rotational structure encoded in the angular momentum vector.
The constraint is non-trivial because angular momentum is a vector, not a scalar. Preserving its magnitude alone would allow the orbital plane to precess under dissipation. Preserving the full vector means the dissipative force must lie in the instantaneous orbital plane of each body, coupling the force direction to the instantaneous velocity in a way that's globally consistent across all N bodies simultaneously. The construction achieves this through a careful decomposition of the velocity into radial and tangential components relative to the center of mass, applying drag only to the tangential part.
The result: orbits circularize (eccentricity decreases) and shrink (semi-major axis decreases) while the orbital plane remains fixed. Energy leaves; geometry stays.