Maple-models of movement of part of a surface of a hyperbolic cylinder
DOI:
https://doi.org/10.31548/energiya2018.02.139Abstract
In many technological processes of agricultural production there is a movement of material particles with rough work surfaces of complex shape. Knowledge of the patterns of motion of a particle (as a material point) with a rough surface of an arbitrary position in a three-dimensional space allows us to calculate the structural and kinematic parameters of the working bodies.
Computer simulation of the motion of a particle with rough surfaces allows to discard cumbersome analytical transformations carried out by a scientist and provide him with a convenient 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 that is in a certain way located in space .
The purpose of the study is the development of the Mapple model of the motion of a particle with the surface of a hyperbolic cylinder ..
Since the analytical calculations of the formation of the laws of motion of a particle by most of the rough surfaces of the second order are rather cumbersome, for these surfaces it is expedient to give only their parametric equations (initial condition) and the law of motion (analytical result) obtained in projections on the orth of the normal N (the force F_N of the normal reactions) and ortes u and v of the OuvN trilogy or the O and T T and P triangles OTPN.
A complex of computational experiments was carried out to study the trajectory-kinematic properties of the particle's motion by the surface of a hyperbolic cylinder under initial conditions: the shape and position of the surface, the place and direction of the casting of the particle, its initial velocity, and the coefficient of friction.
It has been shown that the motion of a particle with a rough surface of hyperbolic cylinders essentially depends not only on the angle of inclination of their rectilinear creations from the vertical position, but also on the angle of position of the axes of the corresponding guide curve - hyperbola.
On the example of forming the laws of motion of a particle with rough non-linear surfaces in the computer algebra Maple environment, the possibility of not displaying a sequence of cumbersome analytic transformations is shown at all. In this case, the user of the model for studying the motion of a particle with a rough surface is sufficient only to set the initial conditions for the particle sinking and to form a set of trajectory and kinematic characteristics studied.
References
Nesvidomin, A.V. (2015). Doslidzhennia rukhu chastynky po shorstkii poverkhni dvoporozhnynnoho hiperboloida obertannia Investigation of the motion of a particle on a rough surface of a two-cavity hyperboloid of rotation ]. [Materialy IV-i mizhnarodnoi naukovo-praktychnoi konferentsii studentiv, aspirantiv ta molodykh vchenykh «Prykladna heometriia, dyzain ta ob’iekty intelektualnoi vlasnostita innovatsiina diialnist». Kiyv.: NTUU «KPI», 172-175.
Pylypaka, S.F. (1998). Kinematychna interpretatsiia rukhu suprovidnykh tryhrannykiv Frene i Darbu cherez vnutrishni parametry kryvykh [Kinematical interpretation of the motion of the accompanying Fresnel and Darboux triangles through the internal parameters of the curves ]. Naukovyi visnyk NAU, 4, 143-146.
Pylypaka, S.F., Nesvidomin, A.V. (2014). Traiektorno-kinematychni vlastyvosti rukhu chastynky po shorstkii poverkhni hiperbolichnoho tsylindra dovilnoho polozhennia [Trajectory-kinematic properties of motion of a particle on a rough surface of a hyperbolic cylinder of arbitrary position]. Suchasni problemy modeliuvannia: zb. nauk prats MDPU im. B. Khmelnytskoho. Melitopol: MDPU, Vol. 2, 76-82.
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