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Generalized geometric projection system mitigates energy growth in gravitational systems, enhancing orbital stability.
Standard numerical splitting schemes applied to multi-body gravitational systems suffer from exponential energy growth due to non-diagonal Coriolis coupling. We present a generalized two-contour geometric projection system PPEC operating in rotating and bi-periodic synodic frames. Extended from the autonomous circular restricted three-body problem (CR3BP) to the non-autonomous bicircular restricted four-body problem (CR4BP), the framework incorporates path-integrated pseudo-Jacobi flux tracking and a two-frequency composite Lie rotation operator R_CR4BP in SO(3). Numerical tests demonstrate strict machine-precision invariant bounding over one hundred thousand primary orbital periods.
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Maksym Koresh (2026) studied this question.
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