Th is paper presents an advanced mathematical model of the “Sich” spacecraft attitude control system, characterized by the integration
of two independent reaction wheel loops: a primary loop optimized for high-speed dynamic maneuvering and a precision
loop dedicated to high-accuracy sub-arcsecond stabilization. Th e primary objective of this study focuses on angular motion control
during key operational stages, including initial damping, three-axis orientation, programmed tracking maneuvers, and orbital
data downlink modes. Th e comprehensive modeling methodology is rigorously based on kinematic equations using quaternions
and Euler’s dynamic equations of rigid-body motion, fully incorporating gravitational, aerodynamic, and magnetic disturbance
torques that realistically refl ect orbital environmental conditions. Special engineering attention is paid to formalizing the nonlinear
switching algorithms between the “coarse” and precision reaction wheel loops during the rapid transition from dynamic
tracking to target imaging operations. New analytical approaches for the computer-aided design of control torque distribution
laws and a synchronized momentum desaturation scheme via electromagnets under a strictly limited spacecraft power budget
are proposed. Comprehensive numerical simulation results, executed with a high-fi delity discrete time step, explicitly demonstrate
the overall eff ectiveness of the developed two-level actuator architecture in achieving high-precision pointing requirements while
maintaining exceptionally low onboard energy consumption. Th e developed mathematical models, computational methods, and
stabilization algorithms are directly intended to support advanced systems design, structural synthesis, and overall optimization of
future generations of Earth observation satellites.