Maple-model of movement of a particle on the inclined plane in the function of the parameter of time
DOI:
https://doi.org/10.31548/energiya2019.04.108Abstract
Abstract. The interaction of the moving particle with the rough surface takes place in many agricultural production processes and has been the subject of much research. 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 particle motion on an inclined plane as a function of time.
The use of 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 in the function of time in the projections on the T and P vertices of the OTPN Darboux trihedron is obtained.
The trajectories r (u) and velocity graphs V (u) of the particle along an inclined plane with different angle of inclination from the vertical position for different throw 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 as a function of time allows us to investigate its trajectory-kinematic properties at a given area of the surface.
The choice of the accompanying trihedron trajectory OuvN or OTPN 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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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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