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High-order analytical solutions of bounded relative motions for Coulomb formation flying

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Abstract

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. A semi-analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equilibrium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt–Poincaré method. The details of the series expansion and coefficient solution for arbitrary \(m\!:\!n\)-period orbits are discussed. To verify the effectiveness of the proposed method, the practical convergence domain of the high-order series solution is computed by comparing it with corresponding numerical solutions that satisfy the specified boundary conditions. Simulation results demonstrate the efficacy of the Lindstedt–Poincaré method in constructing series solutions for the relative motion of Coulomb formation systems.

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Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors acknowledge the financial support from the Shanghai Sailing Program (21YF1417500).

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Authors and Affiliations

  1. School of Aeronautics and Astronautics Sun Yat-sen University, Shenzhen, 518107, China

    Mingpei Lin & Jinxiu Zhang

  2. School of Astronautics Beihang University, Beijing, 100191, China

    Ming Xu

  3. Shanghai Aerospace Control Technology Institute, Shanghai, 201109, China

    Xiao Pan

  4. Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai, 201109, China

    Xiao Pan

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  1. Mingpei Lin
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Contributions

ML contributed to the study conception and Methodology and wrote the first draft of the manuscript. JZ contributed to the study conception and carried out project administration. Investigation is performed by MX. XP provided the funding and the support in writing, review and editing. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Jinxiu Zhang.

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Lin, M., Zhang, J., Xu, M. et al. High-order analytical solutions of bounded relative motions for Coulomb formation flying. Nonlinear Dyn 111, 12931–12946 (2023). https://doi.org/10.1007/s11071-023-08518-3

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