THE MATHEMATICAL MODEL OF A GUIDED CURVILINEAR MOTION TRANSPORTATION-LOADING EQUIPMENT
The problem of modeling managed curvilinear motion of transport and loading facilities, consisting of a tractor-trailer. As a three-tier design scheme chosen pendulum system. When this is considered a curvilinear motion of the system in which the center of gravity of the first shaft (tractor) is moving in a circle. Determined by the governing power points (a pair of forces) in cylindrical hinge connecting the parts of the system, providing stable movement of the second rod (drawbar) and the third bar (trailer) in the vicinity of the circle under consideration. To produce a mathematical model of the process used the Lagrange equations of the second kind. In accordance with the well-known theory rather complex nonlinear differential equations are linearized and are considered small movement (oscillation) of the system. Since we consider the case when the center of gravity of the tractor moves in a circle at a constant speed, it defines the boundary conditions for the solution of differential equations on a fixed time interval. For the case of small motions of the system found control points (a pair of forces) provides the desired motion and the original nonlinear control system, which simulates a tractor-trailer. In this model, as generalized coordinates to determine the position of the pendulum links are corners. In the case of a large amount of time tractor train traffic on this segment of the circle is divided into small intervals and the final position of the system on one segment is the initial position of the system at the next time interval. The proposed design allows for efficient computer simulation of the motion of the “tractor - drawbar - trailef’ in real time. A similar problem was considered by the authors in a simplified form. Here is a refined mathematical model of the considered transport and loading facilities.