In this study the dynamic model of a space robot manipulator is constructed. The space robot manipulator as a three-degree-of-freedom manipulator on a movable base is represented. Functioning of space robotic manipulator near the orbital space station is considered. It is also anticipated that the motion occurs in a weightless environment, without affecting the dissipative forces. On the grounds of this model of space robot manipulator the first problem of the dynamics of the manipulator is solved. The problem is solved using the expansion pack Symbolic Math Toolbox mathematical package Matlab. The results of this study are shown graphically.