Mathematical model of complex movement of a material point on a surface of agricultural machine working body

Abstract

In theoretical study of most of agricultural machines working bodies there is a need of the modeling of material particles (material points) motion on their working surfaces. Questions of such modeling in cases when the specified surfaces are give to material points movement with difficult trajectories are especially difficult. Objective of this research is to develop the basic provisions of complex movement theory of material point. When carrying out research methods of modeling theory, theoretical mechanics, higher mathematics, in particular differential geometry, methods of drawing up programs and numerical calculations on the personal computer are used. As a result of the conducted theoretical research the complex movement of material point which relative movement happens in a moving trihedron of curve which is defined by the natural equations is considered. The figurative movement of a trihedron is defined by differential characteristics of curve. Competency of use of Frenet formulas for finding absolute speed and point acceleration in projections on unit vectors of the moving trihedron is proved. As a result of numerical calculations on the personal computer there were found absolute trajectories of material point movement and qualitative assessment of received results was carried out.