The N-body problem as a research area investigates the dynamics and long-term evolution of systems composed of multiple interacting bodies, typically governed by classical or relativistic gravitational forces, but also by Coulomb or other pairwise potentials in some contexts. It encompasses analytical studies of existence, stability, and chaos in multi-body solutions, as well as the development of numerical integration schemes, regularization techniques, and perturbation methods. Research addresses issues such as secular evolution, resonances, collisional versus collisionless regimes, and scaling algorithms (e.g., tree codes, fast multipole methods), with applications spanning celestial mechanics, stellar dynamics, planetary system formation, and large-scale cosmological simulations.
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