Research of planar motion of spacecraft around its center of mass under the influence of the gravitational and the aerodynamic moments during its descent from circular orbits

The paper deals with the planar motion of an uncontrolled axisymmetric spacecraft around its center of mass under the influence of the gravitational moment and the restoring aerodynamic moment. The restoring aerodynamic moment of the spacecraft is described by an odd Fourier series in the angle of attack with the two first harmonics. The evolution of phase trajectories is studied on the basis of analyzing the action integral. The evolution of the phase trajectories is caused by the descent of the spacecraft from a low circular orbit due to the atmospheric deceleration. The moments of transition between various areas of the phase plane are determined. For the cases of motion, when, intersecting the separatrix, the phase point may fall into various oscillation regions, the formulas for determining the possibility of capture into any region are found.