Spacecraft with Periodic Mass Redistribution: Regular and Chaotic Behaviour

The motion of a spacecraft containing a moving massive point in the central field of Newtonian attraction is considered. Within the framework of the so-called “satellite approximation”, the center of mass of the system is assumed to move in an unperturbed elliptical Keplerian orbit. The spacecraft’s dynamics about its center of mass is studied. Conditions under which the spacecraft rotates about a perpendicular to the plane of the orbit uniformly with respect to the true anomaly are found. Such uniform rotations are achieved using a specially selected rule for changing the position of a massive point with respect to the spacecraft. Necessary conditions for these uniform rotations are studied numerically. An analysis of the nonintegrability of a special class of spacecraft’s rotation is carried out using the method of separatrix splitting. Poincaré sections are constructed for certain parameter values. Several linearly stable periodic motions are pointed out and investigated.