In article the UAV three-dimensional mathematical model on the basis of the quadcopter as most the UAV widespread type at the moment is developed. The quadcopter is based on a frame of DJI F-450. The first part of article is devoted to the mathematical description of the quadrotor model, namely: to a kinematics and dynamics models; to forces and torques operating on the UAV; to rotation matrixes; to the assumptions simplifying mathematical expressions. For the description of location and movement of the quadrotor in space also the bound will be used inertial reference frame. Therefore transformation from one frame to another is necessary. The simulation of the operation of the motors 1-4, which are electric drives of direct current, has been performed. Rotation of engines is transferred to screws directly. Movement of the quadcopter in the bound frame is considered in the article by the accounting of the models of a kinematics and dynamics describing the vehicle movement.

Keywords: quadrotor, UAV, kinematics, dynamics, 3D environment, DJI F-450, engine, traction, rotation matrix, vehicle