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Jorba, À., Jorba-Cuscó, M.: Invariant manifolds near \({L}_1\) and \({L}_2\) in the quasi-bicircular problem. Celestial Mech. Dyn. Astron. 135(15). (2023)Sanaga, R.R., Howell, K.: Analyzing the Challenging Region in the Earth-Moon L\(_2\) Halo Family via Hill Restricted Four-Body Problem Dynamics. In: AIAA SCITECH 2024 Forum, (2024)Sanaga, R.R., Howell, K.C.: Synodic resonant halo orbits in the Hill restricted four-body problem. In: 33rd AAS/AIAA Spaceflight Mechanics Meeting, Austin, Texas, January 15-19, 2023 (2023)Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth-Moon-Sun system. Celest. Mech. Dyn. Astron. 70, 75–98 (1998). ADS MathSciNet MATH Google Scholar Szebehely, V.: Theory of Orbit: The Restricted Problem of Three Bodies. Academic Press (1967). D., Baresi, N., Locoche, S., et al.: Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem. Adv. Space Res. 71(1), 336–354 (2023). ADS Google Scholar Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton University Press (1947)MATH Google Scholar Zimovan-Spreen, E.M., Howell, K.C., Davis, D.C.: Near rectilinear halo orbits and nearby higher-period dynamical structures: orbital stability and resonance properties. Celest. Mech. Dyn. Astron. 132(5), 28 (2020). ADS MathSciNet MATH Google Scholar Zimovan-Spreen, E.M., Scheuerle, S.T., McCarthy, B.P., et al. Baseline Orbit Generation for Near Rectilinear Halo Orbits. In: AAS/AAIA Astrodynamics Specialist Conference, Big Sky, Montana, August 13-17, 2023 (2023)Download referencesAcknowledgementsValuable discussions with members from Multi-Body Dynamics Research Group are appreciated. Beom Park would like to thank Kwanjeong Educational Foundation for the financial support. Rohith Reddy Sanaga would like to thank Department of Computer Science Department at Purdue University. Portions of this work are also supported by Purdue University and under Grant NASA JSC 80NSSC18M0122.Author informationAuthors and AffiliationsSchool of Aeronautics and Astronautics, Purdue University, 610 Purdue Mall, West Lafayette, IN, 47907, USABeom Park, Rohith Reddy Sanaga & Kathleen C. HowellAuthorsBeom ParkYou can also search for this author in PubMed Google ScholarRohith Reddy SanagaYou can also search for this author in PubMed Google ScholarKathleen C. HowellYou can also search for this author in PubMed Google ScholarCorresponding authorCorrespondence to Beom Park.Additional informationPublisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.AppendicesAppendix A Review of the QBCP expressions from Andreu (1998)The expressions that appear in the original derivation of the QBCP from Andreu (1998) are reviewed. A group of coefficients, \(\alpha _{k}\), \(1 \le k \le 8\), appear with the following physical interpretations, (A1) The \(\alpha _{k}\) functions are assumed in the following forms,$$\begin{aligned} \alpha _{k} = \sum _j \alpha _{kj} \cos (j t_*), & k = 1, 3, 4, 6, 7 \nonumber \\ \alpha _{k} = \sum _j \alpha _{kj} \sin (j t_*), & k = 2, 5, 8, \end{aligned}$$ (A2) where sines and cosines coefficients \(\alpha _{kj}\) are included in Tables 3, 4, and 5. Note that

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