Pendulum systems are widely used in space exploration. For example, the model considered in the work of Spencer W. Zigler and Matthew P. Cartmell, belongs to this class of models. In this model, to the satellite hingedly attached dumbbell (cosmic pendulum), with two masses at the ends and the pendulum is driven by a variable torque M (ωt). Dumbbell can perform both the vibrational and rotational motion relative to the center of mass of the satellite. As a rule, similar models are studied by traditional methods (averaging method, the method of small parameter, asymptotic methods), which provide many important results for the practice. Recently, for various strongly nonlinear dynamical systems it is possible to obtain new, previously unknown, qualitative solutions, for example, rare attractors based on the method of complete bifurcation groups. This work is devoted to study of approximate model of the space pendulum by the method of complete bifurcation groups.