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MOVEMENT OF PARTICIPANTS ON THE CURRENT SKIN IN THE CIRCULAR ARCHIMEDA

A. Nesvidomin

In many agricultural processes, there is the movement of material particles on rough work surfaces of complex shape. Understanding the patterns of motion of a particle on a rough surface of arbitrary position in a three-dimensional space allows us to deliberately calculate the structural and kinematic parameters of the working bodies.

Computer simulation of the motion of a particle on rough surfaces allows to discard bulky analytical transformations and provide the scientist with a convenient dialogue mode for carrying out the necessary computational experiments on the analysis of the motion of a particle under different initial conditions of its throw on any rough surface that is in a certain way located in space.

The purpose of the study is to develop, in the environment of a symbolic algebra Maple, a computer model of motion of a particle on a rough cylindrical surface with an orthogonal section in the form of an Archimedid spiral, and, using computational experiments, to find out its trajectory-kinematic properties.

Cylindrical surfaces with spiral orthogonal cross-sections in different ways transport the material depending not only on the shape and position of the surface, but also the direction of their throw - in the direction of twisting or rotation of the spiral. Also, these surfaces allow you to distribute loose material in space between their turns.

Formation of the laws of motion of a particle on the rough interior surface of the Archimedes cylinder is presented in the listing of CylinderArchimedes (see geometry.com.ua).

When using the vertical position of the Archimedean cylinder as a side guard case at a given angle of throwing 90 the smaller the coefficient of friction, the faster this particle begins to recruit the rate of fall

With a horizontal cylinder of Archimedes, with bulge down, all the particles stop on the surface and the very first one that was thrown at an angle of 90 . -

At the cylindrical surface of Archimedees, the upward movement of particles is carried out on the inner surface of the cylinder from below, with some particles can break away from the surface.

Studies have established that a shell of cylindrical shape with an orthogonal cross-section in the form of an Archimedes' spiral, in contrast to the emulsion housing, more intensively stops the movement of particles due to turns.

Pylypaka, S.F., Nesvidomin, A. V. (2011). Avtomatyzatsiia modeliuvannia rukhu chastynky po hravitatsiinykh poverkhniakh na prykladi pokhyloi ploshchyny v systemi Maple [Automation of modeling of a particle motion on gravitational surfaces on an example of an inclined plane in the system Maple]. Prykl. heom. ta inzh. Hraf, 86, 64-69.

Aladyev, V.Z., Boyko, V.K., Rovba, E.A. (2007). Programmirovaniye i razrabotka prilozheniy v Maple [Programming and developing applications in Maple]. Grodno-Tallin, 458.

Nesvidomin A.V. (2011). Modeliuvannia rukhu chastynky po shorstkii vnutrishnii poverkhni horyzontalnoho tsylindra v proektsiiakh na orty lokalnykh system koordynat [Simulation of the motion of a particle on the rough inner surface of a horizontal cylinder in projections on the orcs of local coordinate systems]. Heometrychne ta kompiuterne modeliuvannia. Kharkiv: KhDUKhT, 29, 23-29.

Pylypaka, S.F., Nesvidomin, A. V. (2011). Maple-model rukhu chastynky po shorstkii vnutrishnii poverkhni vertykalnoho tsylindra [Maple-model of motion of a particle on a rough inner surface of a vertical cylinder]. Heometrychne ta kompiuterne modeliuvannia. - Kharkiv: KhDUKhT, 28, 19-24.