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Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

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Category: Content №2 2024

Last Updated on 01 May 2024

Published on 30 November -0001

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Authors:

O.O.Aziukovskyi, orcid.org/0000-0003-1901-4333, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V.Z.Gristchak, orcid.org/0000-0001-8685-3191, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

D.D.Hryshchak, orcid.org/0000-0001-8956-8468, “Culver Aviation”, Kyiv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

K.A.Ziborov, orcid.org/0000-0002-4828-3762, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

S.O.Fedoriachenko, orcid.org/0000-0002-8512-3493, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

D.V.Harkavenko*, orcid.org/0009-0004-5011-9015, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2024, (2): 140 - 144

https://doi.org/10.33271/nvngu/2024-2/140

Abstract:

Purpose. Development of an approximate nonlinear model for the solution of the external ballistics problem with determination of the nonlinear system parameters and development of a methodology for calculating the aerodynamic characteristics of the cargo, located on the external suspension of unmanned aerial vehicle (UAV) in order to increase the efficiency of their delivery to the specified landing target by means of asymptotic approach with given parameters of the studied system and external load.

Methodology. The development of an effective model was carried out using analytical and numerical research algorithms based on a nonlinear system of differential equations in a general form with time-varying coefficients. In order to obtain a solution to the nonlinear problem of external ballistics in a two-dimensional formulation, the assumption of a significant influence of the projection of the velocity function on the ordinate axis in relation to the component on the abscissa axis is introduced. The problem is reduced to the solution of a related system of differential equations with variable coefficients along the corresponding coordinates using the asymptotic approach for a small parameter of the coefficient of frontal aerodynamic resistance. Applied mathematical analysis and modeling have been used for the problem formulation considering studied environmental parameters.

Findings. Analytical dependences of the nonlinear problem of ballistics and application of finite-element analysis (FEA) with respect to the cargo motion from the UAV in the presence of the initial speed and wind load in the plane of motion are proposed. It is shown that the obtained analytical solution is correlated with the direct numerical calculation of the basic differential equation with respect to the ordinate axis.

Originality. A mathematical nonlinear model of the dynamic process is proposed, assuming the prevailing influence of the speed function along the ordinate axis compared to the function along the abscissa axis. To obtain an approximate analytical solution of the basic nonlinear system of differential equations with variable coefficients the asymptotic perturbation method is applied. The dependence for the axial displacement function is presented considering actual time-flight parameter.

Practical value. The obtained analytical dependencies for estimating the time and distance reaching the target with the initial speed of movement and the presence of wind load can be used in applied problems of mathematical physics and engineering calculations of functional dependencies and control of the cargo delivery process and target reaching from an UAV. The obtained analytical results and the solution algorithm can be integrated into applied problems of mathematical physics and engineering calculations, particularly the development of ballistic system control algorithms.

Keywords: ballistics, FEA, mathematical model, dynamics, UAV, perturbation, aerodynamic resistance

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