For modern aircraft of axisymmetric shape, including lander, aeroballistic vehicles, an important condition for regular operation is the absence of asymmetries of various kinds, provided that they were not intentionally introduced during the design and production of the structure. Asymmetries caused by changes in the shapes of the outer surface lead to changes in the massinertial characteristics of the vehicles, displacement of the center of mass, the appearance of centrifugal moments of inertia, the appearance of aerodynamic moments. All this can lead to a deviation of the flight path of the aircraft from the nominal trajectory, to an increase in the loads acting on the structure, due to an increase in the angle of attack, the magnitude of aerodynamic forces and overloads. In addition, asymmetries can lead to resonant phenomena in the process of movement. The paper presents a mathematical model of the motion of an aircraft in the atmosphere, which allows taking into account the displacement of the center of mass, dynamic imbalance and aerodynamic asymmetry. The influence of the displacement of the center of mass, the influence of aerodynamic moments leading to aerodynamic asymmetry on the movement of aircraft without spin stabilization and with spin stabilization has been studied. A law is proposed for displacement of the center of mass of an aircraft in order to create lifting force components, both for correcting disturbances caused by asymmetries, and for spatial maneuvering, which allows smoothly changing the angle of attack and setting the vehicle in the equilibrium position. By numerical simulation of the motion of an aircraft with spin stabilization, the effectiveness of using the displacement of the center of mass to reduce the components of accelerations, angular velocities of rotation and angle of attack is shown.