Periodic orbits with low-thrust propulsion in the restricted three-body problem

Periodic orbits around nonequilibrium points are generated systematically by using continuous low-thrust propulsion in the restricted three-body problem, with a mass ratio varying from 0 to 1/2. A continuous constant acceleration is applied to cancel the gravitational forces of two primary bodies and the centrifugal force at a nonequilibrium point, which is changed into an artificial equilibrium point. The equations of motion are linearized to analytically generate periodic orbits with constant acceleration. Then, periodic orbits around artificial equilibrium points which exist on the line connecting two primary bodies are investigated. The frequencies of these periodic motions are expressed by a parameter that is a function of the mass ratio and the position of the orbits around artificial equilibrium points. By choosing the frequencies of motions that are small-integer resonant, we have found the existence of points at which in-plane and out-of-plane motions are synchronized.