Maple-models of motion of the particle on rough sloping disk given in the polar coordination system
DOI:
https://doi.org/10.31548/energiya2019.02.104Abstract
Abstract. To construct agricultural machinery it is important to know the regularities of the motion of a particle (as a material point) on a rough surface of an arbitrary position in a three-dimensional space, which allows us to calculate the structural and kinematic parameters of the working bodies.
The application of computer modeling of the motion of a particle with rough surfaces allows the discarding of bulky analytical transformations in carrying out 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 Maple-model of motion of a particle on a rough sloping disk.
When studying the motion of a particle on a rough sloping disk, a polar coordinate system was used.
The trajectories of the particle motion on the rough sloping disk have been obtained at various values of the angle of its throw. It is established that under the same initial conditions of the particle throwing, the trajectories of particles on the rough sloping disk are congruent to the trajectories of the particles along a rough sloping plane. At the same time, the position of trajectories relative to the coordinate lines of flat compartments differ considerably.
On the example of the developed model of motion of a particle on a sloping flat disk, it is shown that the trajectories of the particle and its kinematic properties do not depend on the type of parametric determination of the surface.
Keywords: triedrone, material point, rough sloping disk, trajectory of motion
References
Nesvidomin, A. V. (2015). Modeliuvannia rukhu chastynky po shorstkii horyzontalnii ploshchyni, yaka zdiisniuie priamoliniini kolyvalni peremishchennia [Modeling of motion of a particle on a rough horizontal plane, which carries out straight-line oscillatory displacements]. Suchasni problemy modeliuvannia: zb. nauk prats MDPU im. B. Khmelnytskoho, 4,100-104.
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.
Linnyk, M. K., Voitiuk, D. H., Pylypaka, S. F. (2005). Tryhrannyk i formuly Frene v zadachakh kinematyky i dynamiky chastynky u skladnomu rusi [Triangular and Frenne formulas in the problems of kinematics and dynamics of particles in a complex motion]. Naukovyi visnyk Natsionalnoho ahrarnoho universytetu, 80 (1), 271-287.
Pylypaka, S.F., Nesvidomin, A. V. (2011). Traiektorii rukhu chastynok po shorstkii pokhylii ploshchyni pry yikh bokovii podachi [Trajectories of motion of particles on a rough slope plane with their side feed]. Prykl. heom. ta inzh. hraf., 87, 36-41.
Downloads
Published
Issue
Section
License
Relationship between right holders and users shall be governed by the terms of the license Creative Commons Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
