Рух частинки по горизонтальній площині, яка здійснює коливальні переміщення в просторі

Анотація

PARTICLE MOVEMENT BY THE HORIZONTAL PLANE WHICH MAKES VIBRATIONAL DISPLACEMENTS IN SPACE

A. Nesvidomin

The establishment of patterns of motion of a particle on different surfaces allows us to calculate the parameters of many working bodies of agricultural machines. The study of trajectory and kinematic characteristics of the motion of a particle requires the formation of a system of differential equations of the 2 nd order and its approximate solution, which is a rather labor-intensive process and practically impossible to implement without the use of modern packages of symbolic algebras. The expansion of these studies is possible only through the use of modern computer simulation technology.

The purpose of the study is to develop for the environment of the symbolic algebra Maple a computer model of motion of a particle on a horizontal plane, which carries out oscillatory displacements in space, and with the help of computational experiments to find out its trajectory-kinematic properties.

The research was carried out using computer technology to formulate the motion law and analyze the trajectory-kinematic characteristics, comparing them with known results.

Research results. The influence of the initial velocity of the particle flutter affects only the time of stabilization of its motion. In certain ratios of the angular velocity of the crank and the coefficient of friction of the particle it is possible to stop it in an oscillatory plane that is unacceptable for separation.

2. It has been shown that for a horizontal rough plane, which performs reciprocation oscillations, the absolute and relative trajectories of the particle are most rapidly stabilized at the highest friction coefficient. Particles with a lower coefficient of friction have a smaller amplitude of absolute trajectory. The initial velocity and direction of throwing influence the time and place of the stabilization of the movement.

3. The angle of inclination of the rough vibrational plane greatly affects the form of the absolute and relative particle trajectory after stabilizing their displacement-they are zigzag-shaped, whose amplitude depends on the parameters of the oscillation.