Maple-model of movement of participants in a passenger plane in the function of the parameter of its provisions
DOI:
https://doi.org/10.31548/energiya2019.01.149Abstract
In many agricultural technological processes there is movement of material particles on an inclined plane. Understanding the patterns of motion of a particle in the plane 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 allows to discard bulky analytical transformations and provide a 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, which in a certain way is located in space. But the development of computer models of motion of a particle on the surface requires the solution of a number of theoretical and practical issues that make up the relevance of research. First of all, it is the development of a general algorithm for the automatic removal of a system of differential equations of the motion of a particle on any surface arbitrarily located in space; analysis of trajectory-kinematic characteristics of the motion of a particle not only in time, but also the position of the particle and the direction of its movement along the surface; realization of approximate methods of solving systems of differential equations for revealing the results of research in the form of numerical data, graphic images and simulation models of motion of a particle on a surface.
The purpose of the research is to develop Maple-model of motion of a particle on an inclined plane in the function of its position parameter.
Application of accompanying triangles of the particle trajectory allowed us to reduce the law of motion of a particle to a system of two differential equations, the internal ones u, v are the coordinates of the surface of the particle's trajectory.
The law of motion of a particle over a rough sloping plane in the function of positioning it on a plane in projections on the orcs T and P of the Darbu triangular OTPN is obtained.
The trajectories r (u) and graphs of velocities V (u) of the particle on an inclined plane with different angles of its inclination from the vertical position for different angles, initial speed and coefficient of friction are obtained. The motion of the particle under the appropriate initial conditions is analyzed.
Simulation of the motion of a particle on a rough surface in the function of its position allows us to investigate its trajectory-kinematic properties on a given section of the surface.
The choice of the accompanying triangular of the OuvN or OTPN trajectory does not affect the results of the trajectory-kinematic properties of the particle motion, although it is indicated in the sequence of the derivation of its motion law.
References
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