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The article considers the development of a mathematical model of the stabilization and rotation system in the modes of stabilization, targeting, auto-tracking of the target and electrical arrest. The output signals shall be signals proportional to the components of the angular velocities of the line of sight, the angles of pitch and dash of deviation around the axes of the gyrosystem and the angles of inconsistency of the line of sight relative to the optical axis of the homing head. The system of cardan suspension of the stabilization and rotation system is considered, where the actuators are located on the axes of rotation of the outer and inner frames of the cardan suspension. The homing head is mounted on the inner frame. The inner frame is a gyrostabilized platform. Depending on the mode of operation of the stabilization and rotation system: in the stabilization mode, the coordinate system that is stabilized is assumed to be stationary in inertial space; in the auto-tracking mode of the target, the coordinate system that is stabilized by Oxyz is returned according to the change of direction to the target; in the mode of electrical locking, the axes of the coordinate system which is stabilized by Oxyz coincide with the axes of Oxoyozo connected to the body of the main product. To obtain differential equations, the projections of the total vector of the kinetic moment of the inner and outer frames on the axis of the outer frame are taken and written according to the theorem on the change of the kinetic moment of the considered system relative to the axes of suspensions. The total moments of external forces applied to the outer and inner frames around their axes of rotation, which have the following components: moments of actuators, moments of viscous and dry friction, imbalance and other unaccounted for factors around the axes of the outer and inner frames . The moments of the forces of viscous and dry friction are presented in the classical form, taking into account the signs when changing the direction of movement. The mass of the inner frame with all devices mounted on it, and the mass of the entire movable system (outer and inner frames), as well as the radius vector characterizing the displacement of the center of mass, give a static imbalance of the movable system relative to the suspension axis of the i-th frame are components imbalance. The scientific novelty of the work is to obtain a mathematical model for a particular product, as well as the practical feasibility of their application. The result is a differential equation that fully describes this system of stabilization and rotation, takes into account the parameters of actuators, turbulent moments, as well as random effects and can be used depending on the tasks., Рассматривается разработка математической модели системы стабилизации и поворота в режимах стабилизации, целеуказания, автосопровождения цели и электрического аретування. В режиме автосопровождения цели оптический канал определяет координаты отклонения линии визирования по линии цели. Углы целеуказания выдаются относительно системы координат корпуса основного изделия в виде углов Эйлера - заданных углов поворота внешней рамки относительно корпуса и внутренней рамки относительно внешней., Розглядається розробка математичної моделі системи стабілізації і повороту в режимах стабілізації, цілевказівки, автосупроводу цілі та електричного аретування. В режимі автосупроводу цілі оптичний канал визначає координати відхилення лінії візування щодо лінії цілі. Кути цілевказівки видаються відносно системи координат корпусу основного виробу у вигляді кутів Ейлера – заданих кутів повороту зовнішньої рамки відносно корпусу і внутрішньої рамки відносно зовнішньої.