A mathematical dynamic model of a closed hydraulic system for controlling speed changes through a gear differential, which consists of a motor, a gear transmission, a gear hydraulic pump, a closed-loop pipeline, and a control valve, is obtained. The engine can be a solar gear, or an epicycle, or a gear differential, and with the help of a closed hydraulic system, you can change the speed of the solar gear, or an epicycle, or a carrier from when the gear pump pumps fluid in a closed pipe. when the pipeline is closed by the regulating crane, the gear hydraulic pump will be stopped and the link on which the closed hydraulic system is installed will be stopped. The result is an analytical expression to determine the speed of the fluid in a closed hydraulic system, which depends on the angular velocity of the enginethe control links of the solar gear, or epicycle, or carrier.