Construction of a Linear Surface According to the Calculated Trajectory of the Movement of a Material Particle Along It

Abstract

Currently, studies of the movement of agricultural materials on gravity surfaces have been carried out. These works also indicate the possibility of solving the inverse problem - the construction of such a surface that would ensure the given trajectory of the particle's movement. In the article, we will consider the construction of a linear surface, which ensures the movement of a particle along a slant line. The property of such lines is a constant angle between the tangent line drawn to the curve at any point and the horizontal plane (the angle of rise of the curve), as well as the parallelism of the main normal of the curve to the horizontal plane The purpose of the research is to construct a linear surface according to the calculated trajectory of the movement of a material particle along it. The construction of a linear surface according to a given trajectory of the movement of a material particle under the action of the force of its own weight is considered. A system of equations was obtained that describes the movement of a material particle along a linear gravitational surface. The considered example is the construction of a linear surface, which, with a known coefficient of friction, would ensure the movement of a particle along a helical line given by the angle of elevation and a constant curvature. An example of the construction of a linear surface is also given, which, with a known coefficient of friction, would ensure the accelerated movement of a particle along the surface with a constant angle. The results of the conducted research make it possible to construct a linear surface according to a given trajectory of the movement of a material particle under the action of its own weight.