What question did this study set out to answer?

This note explores structural connections between the COCM orbital framework and periodic orbit theory. The goal is to propose new hypotheses related to orbital stability and resonant frequencies.

May 31, 2026Open Access

NT17-B: Resonance Structure and Orbital Stability in the COCM — Two Ideas from Periodic Orbit Theory

Key Points

This note explores structural connections between the COCM orbital framework and periodic orbit theory. The goal is to propose new hypotheses related to orbital stability and resonant frequencies.
Developed two analogies between the COCM and periodic orbit theory.
Mapped stability taxonomy onto the COCM (e,n) parameter space.
Proposed a resonant frequency based on the bulk-brane-ring system.
Identified a mapping between S/U/DU/CU taxonomy and the COCM parameter space.
Proposed ω_z = 11.1991 as a significant resonant frequency in the context of the models.

Abstract

This note develops two structural analogies between the COCM orbital framework and periodic orbit theory in the elliptic restricted three-body problem. Analogy 1: the S/U/DU/CU stability taxonomy maps onto the COCM (e, n) parameter space, with the rule that S and DU are never adjacent. Analogy 2: ωᵦ = 11. 1991 is proposed as a resonant frequency of the bulk-brane-ring system, with the e-independence of ncrit (NT17-A) as supporting evidence. Both analogies are stated as working hypotheses; neither is derived from the COCM action.

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