Spatial circular restricted three-body problem (SCRTP) in sidereal cylindrical coordinates system

In the present paper, the equations of motion for the SCRTP in sidereal cylindrical coordinates system were established. Initial value procedure was given together with a numerical example and graphical representations of the variations of the two sidereal coordinate systems, Cartesian (x, y, z) and cylindrical (u₁, u₂, u₃). Many experimentations, show that, the usages of sidereal cylindrical coordinate system in the three body-problem lead to a wonderful property which is: the variations of the sidereal cylindrical coordinates during the orbital motion are very small in comparison to the corresponding variations of the Cartesian sidereal coordinates, a property which produces more stable numerical integration procedures.