Erratum: Kozai mechanism inside mean motion resonances in the 3-dimensional phase space (Monthly Notices of the Royal Astronomical Society (2020) 493 (5816) DOI: 10.1093/mnras/staa684)

The paper 'Kozai Mechanism insideMeanMotion Resonances in the 3-Dimensional Phase Space' was published in Mon. Not. R. Astron. Soc. 493(4): 5816-5824 (2020). In that paper, we have derived that in the circular restricted three-body problem (CRTBP), the Keplerian term of the Hamiltonian for the mean motion resonance (MMR) can be simplified to [equation presented] Based on the modified Delaunay variables and the set of canonical action-angle variables defined in that paper, strictly speaking, H0 should be a function of a rather than a function of a, e and i in Qi & de Ruiter (2020), i.e. H0(a). Since the constant N can be expressed by (Equation Presented) the inclination i can be substituted by a and e. The Hamiltonian H can be expressed by [equation presented] If we fix a, H can be approximately simplified into (Equation Presented) It should be noted that this H(e,ω, ψ) is a pseudo Hamiltonian and not a constant, because the real a is time-varying in the CRTBP. In Qi & de Ruiter (2020), we wrongly claimed that H(e,ω, ψ) is the Hamiltonian and constant. However, since the variation of a is quite small for MMRs in question, H defined in Equation (4) is approximately equal to the real Hamiltonian and we can still investigate the Kozai dynamics inside the MMR by analysing the H structures in the (e,ω, ψ) phase space.We want to emphasise that all results and conclusions obtained from the above semi-analytical remain unchanged, and are actually correct.