Generalized periodic orbits in some restricted three-body problems

Abstract

We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of Boscaggin et al. (Trans Am Math Soc 372: 677–703, 2019) is applicable. This guarantees the existence of an arbitrary large number of generalized periodic orbits (periodic orbits with possible double collisions regularized) provided the mass ratio of the primaries is small enough.

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Acknowledgements

R. O. is supported by MTM2017-82348-C2-1-P. L. Z. is supported by DFG ZH 605/1-1.

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Correspondence to Lei Zhao.

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Ortega, R., Zhao, L. Generalized periodic orbits in some restricted three-body problems. Z. Angew. Math. Phys. 72, 40 (2021). https://doi.org/10.1007/s00033-021-01470-5

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Keywords

  • Forced Kepler problem
  • Restricted three-body problem
  • Generalized periodic orbits
  • Kustaanheimo–Stiefel Regularization

Mathematics Subject Classification

  • 70F15
  • 70F16