What question did this study set out to answer?

To address the systematic drift in fundamental integrals of motion in long-term numerical integration of the N-body problem.

August 11, 2026Open Access

A Global Quasi-Symplectic Projection Method for the Spatial N-Body Problem: Explicit Preservation of Poincaré–Noether Invariants with O(N) Complexity

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Randomized trial demonstrates invariant preservation in N-body systems, suggesting improved long-term integration strategies.

To address the systematic drift in fundamental integrals of motion in long-term numerical integration of the N-body problem.
Developed a global quasi-symplectic projector method to rectify phase-space trajectories.
Used Cartesian vector operations and Rodrigues rotation for algorithm formulation.
Performed numerical experiments on a hierarchical triple system with an eccentric orbit.
The method preserves Poincaré-Noether invariants with machine precision (~10^-15).
Achieved less than 5% computational overhead while maintaining O(N) complexity.
Effectively suppressed secular chaos in the tested orbital mechanics system.

Maksym Koresh (2026) studied this question.

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