Maple-моделі руху частинки поповерхні конуса обертання

Abstract

In many agricultural processes, the movement of particles of material takes place on rough work surfaces of complex shape, in particular, on the surface of the cone of rotation. Understanding the patterns of the motion of a particle (as a material point) on a rough surface of a position in a three-dimensional space allows one to deliberately calculate the structural and kinematic parameters of the working bodies. An analytical derivation of the law of motion of a particle on any rough surface reduces to the compilation of a system of differential equations of the second order. The sequence of analytic transformations of the derivation of the system of differential equations and the methods of its solution is rather laborious. Computer simulation of the motion of a particle on rough surfaces allows to discard bulky analytical transformations carried out by a scientist and provide him with a convenient dialogue mode for carrying out the necessary computational experiments on the analysis of the motion of a particle under various initial conditions of its throw on any rough surface that is in a certain way located in space . The purpose of the research is the development of Mapple-model of the motion of a particle along the surface of the cone of rotation. The developed computer toolkit can be applied in the study of the motion of the particle on the surface of the cone of rotation. Since the analytical calculations of the formation of the laws of motion of a particle are rather cumbersome, only their parametric equations (initial condition) will be given for these surfaces and the law of motion (analytical result) is obtained in projections on the norm of the norm N (the force F n of the normal reaction) and the ort u and v OuvN triangles or the ort T and P triangles. The trajectory-kinematic properties of the motion of a particle on the surface of the cone of rotation are given. For the cone of rotation, from all possible combinations in form and position in space, trajectories and graphs of the particle velocity along its inner surface were constructed when the axis of the cone is inclined at an angle of 45 ° and one of its straight lines is horizontally. In this case, for example, it is shown, in particular, the closer the place of throwing a particle to the top of the cone, the faster it will stop within the limits of the horizontal creature. Keywords: accompanying triangular, material point, cone of rotation, trajectory of motion