Maple-model of movement of particle on an included plane in the function of parameter of movement
DOI:
https://doi.org/10.31548/energiya2019.03.114Abstract
Abstract. In many technological processes of agricultural production there is a movement of particles of material on an inclined plane. Determination of the laws of motion of a particle on the plane of an arbitrary position in three-dimensional space allows to perform the calculation of structural-kinematic parameters of the working bodies.
Computer simulation of particle motion allows to replace cumbersome analytical transformations and provide a dialog mode for carrying out the necessary computational experiments to analyze the motion of a particle under different initial conditions of its throwing on any rough surface, which is in a certain way located in space.
The purpose of the study is to develop a Maple-model of the motion of a particle on an inclined plane as a function of its motion parameter.
The use of the the Darboux trihedron allowed to reduce the law of motion of a particle to a system of two differential equations to determine the velocity and curvature of the particle trajectory.
The law of motion of a particle along a rough inclined plane was obtained in the function of it`s motion on a plane in projections to the T and P orts of the Darboux trihedron
The trajectories and velocity graphs of a particle along an inclined plane with a different angle of inclination from the vertical position for different throwing angle, initial velocity and coefficient of friction were obtained. The particle motion under appropriate initial conditions is analyzed.
Simulation of the motion of a particle on a rough surface in the function of its motion allows to study its trajectory-kinematic properties on a given area of the surface.
The choice of the accompanying trihedron of trajectory or does not affect the obtained results of the trajectory-kinematic properties of the motion of the particle, although it is indicated in the sequence of derivation of its law of motion.
Key words: accompanying trihedron, material point, inclined plane, trajectory of motion
References
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Alad’yev, V. Z., Boyko, V. K., Rovba, E. A. (2007). Programmirovaniye i razrabotka prilozheniy v Maple [Programming and application development in Maple]. Grodno-Tallin, 458.
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. Kyiv: KNUBA, 86, 64-69.
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