Construction of a linear surface according to the calculated trajectory of the movement of a material particle along it
DOI:
https://doi.org/10.31548/energiya2022.03.073Abstract
The construction of a linear surface, which ensures the movement of a particle along a slope line, is considered. A 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 elevation of the curve), as well as the parallelism of the main normal of the curve to the horizontal plane.
Currently, studies of the movement of agricultural materials on working surfaces have been carried out. They showed the possibility of solving the inverse problem - designing a surface that would ensure a given trajectory of the particle's movement.
The purpose of the study is to construct a linear surface along a given trajectory of movement of a material particle under the action of its own weight.
A system of equations is obtained that describes the movement of a material particle along a linear gravitational surface.
Differential equations are solved. Specific examples are given.
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, as well as a linear surface, which, with a known coefficient of friction, would ensure the accelerated movement of a particle along a surface with a constant angle was constructed.
Key words: linear surface, trajectory of movement of a material particle, accompanying Frenet trihedron
References
Voitiuk, D. H., Pylypaka, S. F. (2001). Konstruiuvannia prostorovoi kryvoi linii iz zadanoiu kryvynoiu, yak traiektorii rukhu materialnoi tochky [Construction of a spatial curve of a line with a given curvature as a trajectory of a material point]. Zbirnyk naukovykh prats Natsionalnoho ahrarnoho universytetu “Mekhanizatsiia silskohospodarskoho vyrobnytstva”, 10, 74-78.
Vasilenko, P. M. (1960). Teoriya dvizheniya chastitsy po sherokhovatym poverkhnostyam sel’skokhozyaystvennykh mashin [Theory of particle motion on rough surfaces of agricultural machines]. Kyiv: UASKhN, 283.
/ Zaika P. M. (1992). Izbrann·yye zadachi zemledel'cheskoy mekhaniki [Selected tasks of agricultural mechanics]. Kyiv: Izd-vo USKHA, 507.
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