Consideration was given to derivation of the motion equations of a space robotic module with a mathematical model having many degrees of freedom whose number can vary in the course of operation. This problem was solved in a computing environment such as the Maple program package. It was anticipated that the on-line mathematical model would be used to establish a rational in a sense motion control law of such a complicated object. For this purpose the paper solved some problems of decomposition of the resulting mathematical model. The results of computer-aided derivation of the motion equations of several particular schemes of the of the space robotic module were presented to illustrate constructiveness of the proposed mathematical support of problem solution.