MATHEMATICAL MODELING OF THE ROTATION PHASE OF A SOLID BODY MOVEMENT WHEN DESCENDING FROM THE INCLINED RAMP

Abstract

Known mathematical models of solids coming off a conveyor belt or sloping ramp are based on the construction of three differential equation systems in a rectangular Cartesian system of coordinates. However, there are no results of calculations of motion parameters using these models and their comparison with other calculation and experimental data for specific objects in open print. The aim of the work is to build and test a new adequate mathematical model of the phase of rotation of solid movement when coming down from the sloping ramp to study the parameters of its movement at the beginning of free fall. The task of the solid body rotation phase (a convergence from the supporting surface with a growing angle of inclination from the moment when the center of the body mass is above the edge of the support, to the detachment from the support of its rear end) is considered, which is simulated by a straight homogeneous rod, when descending from the inclined ramp in the polar coordinate system. Differential equations of the rod movement are made with the help of Lagrange equations of the second kind. The generalized coordinates are the distance