The possibility to apply the Frenet trihedron and formulas for the complex movement of a point on a plane with the predefined plane displacement

Material particles interact with the working moving surfaces of machines in various technological processes. Mechanics considers a technique to describe movement point and decompose speed acceleration into single unit vectors accompanying trajectory trihedron for simple movement. The shape spatial curve uniquely sets Frenet trihedral as solid body. This paper has considered relative material particle static plane trihedron, which moves along flat variable curvature. formulas were used build system differential equations In contrast conventional approach, chosen independent was not time but length arc guide moves. been built projections onto trihedron; it solved by numerical methods. use coordinate makes possible solve problems complex point. assigned parametric its function determines portable system. approach enables setting osculating curvature, thereby revealing additional possibilities solving on at rotational motion around fixed axis is partial case. proposed using an example cargo body truck road curvilinear charts slip predefined have constructed