At present, the methods based on using linearized dynamical equations are applied for synthesis of an attitude control system of a satellite with nonlinear dynamics. Linearized equations describe the satellite dynamics approximately, which is the main their disadvantage. This article shows that basing on the angular momentum theorem, the nonlinear dynamical equations of the satellite attitude control system can be represented in the form of linear differential equations with variable coefficients, which makes it possible to use engineering methods of stability analysis and analysis of transient quality in the process of synthesis of the satellite attitude control system.