Modelling of dynamic processes in a nonholonomic system in the form of Gibbs-Appell equations on the example of a ball mill

Volodymyr Shatokhin; Yaroslav Ivanchuk; Vitaly Liman; Sergii Komar; Oleksii Kozlovskyi

doi:10.35784/iapgos.7570

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Published: Dec 20, 2025

DOI: https://doi.org/10.35784/iapgos.7570

Issue Vol. 15 No. 4 (2025)

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DOI

https://doi.org/10.35784/iapgos.7570

Authors

Volodymyr Shatokhin

shatokhinvlm@gmail.com

O. M. Beketov National University of Urban Economy in Kharkiv, Ukraine

https://orcid.org/0000-0002-0766-4104

Yaroslav Ivanchuk

ivanchuck@ukr.net

Vinnytsia National Technical University, Ukraine

https://orcid.org/0000-0002-4775-6505

Vitaly Liman

limanv@ukr.net

Vinnytsia National Agrarian University, Ukraine

https://orcid.org/0000-0003-1280-237X

Sergii Komar

sergey.komar.kh@gmail.com

Ivan Kozhedub Kharkiv National University of the Air Force, Ukraine

https://orcid.org/0000-0002-8961-2614

Oleksii Kozlovskyi

ak@vin.ua

Vinnytsia National Technical University, Ukraine

https://orcid.org/0009-0008-1797-4086

Abstract

In the article the actual scientific and practical problem of creation of the universal mathematical model of dynamic processes in the shockless model of the ball mill is solved. This allowed to determine the technological qualities of the device and to make an effective choice of its rational parameters. Computational studies have been carried out using the developed model by means of computer calculations. As a result, important regularities of the influence of parameters on the technological indicators of the technological device have been established. The result of the study is the first development of a nonholonomic mathematical model of dynamic processes in a ball mill, presented in the form of Gibbs-Appell equations. It is shown that the calculation of the acceleration energy and the formulation of the equations of motion are significantly simplified when quasi-accelerations are used instead of generalised acceleration equations. The developed mathematical model allows to calculate the trajectories of the contact point of the ball with the surface of the spherical chamber, the compressive forces of interaction with the surface of the shell. The results of the mathematical modelling allow efficient selection of rational parameters of the process equipment from the technological point of view.

Keywords:

ball milling, dynamic system, mathematical model, differential equations, velocity, acceleration

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Shatokhin, V., Ivanchuk, Y., Liman, V., Komar, S., & Kozlovskyi, O. (2025). Modelling of dynamic processes in a nonholonomic system in the form of Gibbs-Appell equations on the example of a ball mill. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 15(4), 32–38. https://doi.org/10.35784/iapgos.7570

Modelling of dynamic processes in a nonholonomic system in the form of Gibbs-Appell equations on the example of a ball mill

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