A problem concerned with studying of dynamics of angular motion of large space structures and flexible spacecraft was considered. It stems from the need to take into account multiple elastic modes when analyzing and designing their control systems. It was proposed to seek a solution to this problem, which is especially noticeable when modeling processes with high-frequency oscillations, on the way to replacing the precise solution of the equations of these motions by an approximate solution, that is, to determine a relatively low-frequency envelope of the precise solution, which allows one to extend the step of integration and, therefore, reduce the time of modeling. Two approaches to estimating the envelop were proposed, and their efficiencies were compared by the example of modeling angular stabilization of the flexible satellite with five elastic modes.