Вибір супровідного тригранника для комп’ютерного моделювання траєкторії частинки на поверхні

Abstract

In many technological processes of agricultural production there is an interaction of a moving particle with a rough surface. Determining the patterns of motion of a particle in the plane of an arbitrary position in three-dimensional space allows the calculation of structural and kinematic parameters of the working bodies. Computer simulation of particle motion allows you to replace cumbersome analytical transformations and provide a dialog mode for the necessary computational experiments to analyze the motion of a particle under different initial conditions of its throwing on any rough surface, which is in some way located in space. The purpose of the study is to determine the accompanying trihedron for computer modeling of the particle trajectory on the surface. It is established that the application of the accompanying trihedron of the particle trajectory allowed to reduce the law of particle motion to a system of two differential equations, the sought ones of which are the internal u, v - coordinates of the particle trajectory surface. The trajectory of the particle r in the Cartesian coordinate system Oxyz is obtained by substituting the found u, v - coordinates to the equation R (u, v) of the surface. The choice of the reference system OuvN or OTPN in the formation of the laws of motion of the particle on the surface affects the appearance of systems of differential equations, but the results of their solution when choosing a specific independent parameter will be the same. Key words: accompanying trihedron, material point, frame of reference, trajectory