Maple-models of motion of the particle on rough sloping disk given in the polar coordination system

Abstract

To construct agricultural machinery it is important to know the regularities of the motion of a particle (as a material point) on a rough surface of an arbitrary position in a three-dimensional space, which allows us to calculate the structural and kinematic parameters of the working bodies. The application of computer modeling of the motion of a particle with rough surfaces allows the discarding of bulky analytical transformations in carrying out computational experiments on the analysis of the motion of a particle under different initial conditions of its throw on any rough surface that is in a certain way located in space. The purpose of the study is the development of Maple-model of motion of a particle on a rough sloping disk. When studying the motion of a particle on a rough sloping disk, a polar coordinate system was used. The trajectories of the particle motion on the rough sloping disk have been obtained at various values of the angle of its throw . It is established that under the same initial conditions of the particle throwing, the trajectories of particles on the rough sloping disk are congruent to the trajectories of the particles along a rough sloping plane. At the same time, the position of trajectories relative to the coordinate lines of flat compartments differ considerably. On the example of the developed model of motion of a particle on a sloping flat disk, it is shown that the trajectories of the particle and its kinematic properties do not depend on the type of parametric determination of the surface. Key words: tri edrone , material point, rough sloping disk, trajectory of motion