Modeling of the particle motion trajectory on the surface in its internal coordinates

Abstract

In many technological processes of agricultural production there is an interaction of the moving particle with the rough surface. Determination of the laws of motion of a particle on the plane of an arbitrary position in three-dimensional space allows to perform the calculation of structural-kinematic parameters of the working bodies. Computer simulation of particle motion allows to replace cumbersome analytical transformations and provide a dialog mode for carrying out 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 a certain way located in space. The purpose of the study is to model the trajectory of motion of a particle on a surface in its internal coordinates. The general algorithm for modeling the motion of a particle on an arbitrary surface is based on its internal geometry, which is expressed by the coefficients of quadratic shapes, curved lines on the surface, and accompanying triangles. The paper describes the formation of a particle trajectory on a surface in its internal coordinates. Various approaches to the formation of the trajectory of the particle in the inner , - curvilinear coordinates of the surface have been considered, which have their peculiarities by controlling its independent parameter: time , , , direction of motion , . The given equations of the trajectories , , , and in the inner - coordinates of the surface are necessary and sufficient to determine in the general form their trajectory-kinematic characteristics, respectively, in the function of independent parameters , , , and . Key words: material point, trajectory of motion, internal coordinates