Extensions of Brown Hamiltonian–III. Applications to irregular satellites of giant planets

ABSTRACT Irregular satellites, orbiting at large distances from their host planets, are subject to strong solar perturbations that render long-term orbital predictions particularly challenging. Building upon the extended Brown Hamiltonian framework developed in Paper I, we introduce the modified Lidov integral ($C_{\rm ZLK}$) as a practical diagnostic index to characterize the dynamical modes. We demonstrate that a satellite is trapped inside the von Zeipel–Lidov–Kozai (ZLK) resonance when $C_{\rm ZLK} \lt 0$. Applying this criterion to the known population of irregular satellites, we identify 27 candidates in libration. Direct N-body simulations confirm 26 of these predictions, with the sole exception of S/2019 S1, whose discrepancy is attributed to its proximity to the separatrix. These results establish $C_{\rm ZLK}$ as a decisive parameter for identifying the ZLK resonance, providing an efficient tool for analyzing the secular dynamics in weakly hierarchical three-body systems.