科研之友
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摘要
For the circular restricted three-body problem (CR3BP) in the inertial frame, we interpret the fact that there is no non-trivial 2 pi-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 Poincare'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.
