This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.