Maple-model of particle movement in vertical plane in time function
DOI:
https://doi.org/10.31548/energiya2019.05.149Abstract
Abstract. In many technological processes of agricultural production there is an interaction of the moving particle with the rough surface. 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 some way located in space.
The purpose of the study is to develop a Maple model of particle motion in the vertical plane as a function of time.
The use of the Darbu's accompanying triangular 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 vertical plane as a function of time in the projections of the T and P orthogs of the Darbu OTPN is obtained.
The trajectories r (u) and velocity graphs V (u) of the particle in the vertical plane were obtained for different tilt angle, initial velocity, and friction coefficient. The particle motion under appropriate initial conditions is analyzed.
Simulation of the motion of a particle on a vertical surface as a function of time allows to study its trajectory-kinematic properties on a given area of the surface.
The choice of the accompanying triangular 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 motion law.
Key words: accompanying triangle, material point, vertical plane, trajectory of motion
References
Adamchuk, V. V. (2010). Teoriya tsentrobezhnykh rabochikh organov mashin dlya vneseniya mineral’nykh udobreniy: monografiya [Theory of centrifugal working bodies of machines for the application of mineral fertilizers]. Kyiv: Agrarna nauka, 178.
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.
Nesvidomin, A.V. (2015). Modeliuvannia rukhu chastynky po shorstkii horyzontalnii ploshchyni, yaka zdiisniuie priamoliniini kolyvalni peremishchennia [Simulation of particle motion along a rough horizontal plane that performs linear vibrational displacements]. Suchasni problemy modeliuvannia: zb. nauk prats MDPU im. B. Khmelnytskoho, 4, 100-104.
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