**Andrzej Marczuk 1, Jacek Caban 1,\*, Alexey V. Aleshkin 2, Petr A. Savinykh 2, Alexey Y. Isupov <sup>2</sup> and Ilya I. Ivanov <sup>3</sup>**


Received: 11 August 2019; Accepted: 30 August 2019; Published: 6 September 2019

**Abstract:** The article presents approaches to the formation of a general computational scheme for modeling (simulating) the particle motion on an axisymmetric rotating curved surface with a vertical axis of rotation. To describe the complex particle motion over a given surface, the fundamental equation of particle dynamics in a non-inertial reference frame was used, and by projecting it onto the axes of cylindrical coordinates, the Lagrange's differential equations of the first kind were obtained. According to the proposed algorithm in C#, an application was developed that enables graphical and numerical control of the calculation results. The program interface contains six screen forms with tabular baseline data (input) and a table of a step-by-step calculation of results (output); particle displacement, velocity, and acceleration diagrams constructed along the axes of the system of cylindrical coordinates ρ and *z*; graphical presentation of the generate of the surface of revolution and the trajectory of the absolute motion of a particle over the axisymmetric rotating surface developed in polar coordinates. Examples of the calculation of the particle motion are presented. The obtained results can be used for the study and design of machines, for example, centrifugal rotary chopper machines.

**Keywords:** accelerator; axisymmetric surface; general equation of dynamics; non-inertial reference frame
