RESEARCH OF THE COMPLEX MOTION OF A POINT ON A PLANE BY MEANS OF THE TRIANGLE AND FRENE’S FORMULAS

The interaction of the particles of the technological material with the working moving surfaces of the machines occurs during various technological processes. In the process of such interaction, the particles are forced to slide along the surface in a certain way in relative motion and describe a different trajectory in absolute motion. The absolute trajectory is the geometric sum of the relative sliding motion of the particle and the translational motion of the surface. To add these movements, it is convenient to use two coordinate systems: a moving one, in relation to which the relative movement of the particle is described, and a stationary one, in relation to which the translational movement of the surface and the absolute movement of the particle are described. A study of the relative motion of a particle in the tangent plane of the accompanying Frenet trihedron, which moves along a flat curve with variable curvature, was carried out. The relative motion of a particle in the tangent plane of the accompanying Frenet trihedron, which moves along a flat curve with variable curvature, is considered. Frenet's formulas were used to compile the system of differential equations of the relative motion of the particle. In this regard, unlike the traditional approach, the independent variable was not time, but the length of the arc of the guide curve along which the trihedron moves. The system of equations was composed in projections onto the vertices of a movable trihedron. It was solved by numerical methods. The proposed approach is considered on the example of the relative movement of a load in the car moving along a road with a curvilinear axis of variable curvature. The graphs of the relative sliding trajectory of the load and the relative speed for the given speed of the car were plotted.