Global families of periodic orbits adjacent to libration points in the restricted three-body problem

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Abstract

The restricted circular three-body problem is studied. All global families of periodic orbits adjacent to the libration points are found. A scenario for the evolution of orbits in the family is given. Chains of global families will be highlighted; the chain begins at the triangular libration point, contains global families for the triangular and all collinear libration points, and ends with a family whose orbits are pressed against the main bodies. The evolution of global families in the chain associated with changes in the energy of the system is described. Planar and spatial orbits are studied.

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About the authors

V. N. Tkhai

Institute of Control Sciences of Russian Academy of Sciences

Author for correspondence.
Email: tkhai@ipu.ru
Russian Federation, Moscow

References

  1. Л. Эйлер, Новая теория движения Луны (Л.: Изд-во АН СССР, 1934).
  2. V. Szebehely, Theory of Orbits (New York: Academic Press, 1967).
  3. В.Н. Тхай, Прикладная математика и механика 42, 1026 (1978).
  4. А.М. Ляпунов, Общая задача об устойчивости движения, Cобр. соч. Т. 2 (М.: Изд-во АН СССР, 1956).
  5. Г.Н. Дубошин, Небесная механика. Аналитические и качественные методы (М.: Наука, 1964).
  6. A.A. Zevin, Nonlinear Analysis, Theory, Methods and Appl. 28(9), 1499 (1997).
  7. A.A. Zevin, Nonlinearity 12, 1339 (1999).
  8. В.Н. Тхай, Прикладная математика и механика 55, 56 (1998).
  9. В.Н. Тхай, Вестн. СПбГУ. Сер. 1. Математика. Механика. Астрономия. № 4, 709 (2021).
  10. V.N. Tkhai, in 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference), held on June 1–3, 2022 in Moscow, Russia (IEEE Xplore, 2022), INSPEC Accession Number: 21844085.
  11. В.Н. Тхай, Изв. РАН. Механика твердого тела № 6, 197 (2023).
  12. В.Н. Тхай, Автоматика и телемеханика № 5, 22 (2023).
  13. V.N. Tkhai, in 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference), held on June 3–5, 2020 in Moscow, Russia (IEEE Xplore, 2020), INSPEC Accession Number: 19772903.
  14. В.Н. Тхай, Прикладная математика и механика 55, 578 (1991).

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2. Fig. 1. Curve G of zero velocity on the orbits of the global family intersecting the Hill curves

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