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Title: A study on periodic solutions for the circular restricted three-body problem

For the circular restricted three-body problem (CR3BP) in the inertial frame, we interpret the fact that there is no non-trivial 2π-periodic solution of the problem's homogeneous system. Furthermore, based on Reissig's theory, the existence of periodic solutions for the CR3BP is proved rigorously by using the above fact in conjunction with an a priori estimate. It is significant that the existence of periodic solutions of the CR3BP is mainly influenced by factors such as initial values, primary masses, and selection of the problem's control function. In addition, it is notable that the analytic proof of Poincaré's first class solutions is addressed for all values of the mass parameter in the interval (0, 1), the value of which must be sufficiently small according to previously published literature.
Authors:
 [1] ;  [2]
  1. School of Mathematical Science, Yangzhou University, Yangzhou 225002 (China)
  2. College of Mechanical Engineering, Beijing University of Technology, Beijing 100124 China (China)
Publication Date:
OSTI Identifier:
22342187
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (New York, N.Y. Online); Journal Volume: 148; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTEROIDS; COMPUTERIZED SIMULATION; CONTROL; MASS; MATHEMATICAL SOLUTIONS; PERIODICITY; PLANETS; THREE-BODY PROBLEM