The paper presents study results of the nonlinear interaction processes between the supporting surface of the track Assembly and the ground in the contact patch, using the mathematical models of friction. For the case blaskapelle motion of a caterpillar, when the resultant of the elementary friction forces is limited by the coupling due to the sliding tracks on the ground, it appears that the increase of the lateral component leads to a decrease of the longitudinal component and the change of direction of the resulting force. As a result, with increasing angular velocity of the tracked vehicle a longitudinal component of the friction force decreases, which is the geometric factor and is defined by the locus of friction for a given type of soil. In the development of this well-known model is considered the general case of friction, which describes the effect of reducing the coefficient of friction in the contact patch at increasing the angular velocity of rotation. To describe this process is used the model of the combined friction which occurs when the surface of the body is doing at the same time the rotational and translational motion. The resulting expression for the resultant of forces of friction and the moment of resistance to rotation based on the decomposition of the first order Pade for a flat spot track Assembly with ground of rectangular shape. With combined friction any arbitrarily small perturbation force acting parallel to the surface of the contact spot, leads to slip. The paper considers the possibility of using the model of the combined friction to research a sustainability curvilinear motion of tracked vehicles. The proposed motion of the machine in the mode of skidding on the basis of the frictionslip. The interpretation of the physical processes occurring in the contact area, on the basis of the theory of the combined friction would allow using this mathematical model in the algorithm structure of automatic traffic control for solving the problem of controllability of partial lateral drift that will further improve the mobility and maneuverable quality of tracked vehicles.