The periodic orbits in circular restricted 3-body problem are calculated by different numerical as well as analytical methods. The efficiency of both kinds are compared in this contribution. The improvement of analytical methods can be achieved by an artificial splitting of perturbation term. The analytical approximations are thus sufficiently accurate even for large values of mass ratio μ. The use of these approximations as a zero-order approximation In numerical codes for search for periodic orbits improves their efficiency also.
Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity of this system are analyzed through Poincaré compactification. The simulation results demonstrate feasibility of periodic parametric perturbation control technology and correctness of the theoretical results.