| Issue |
E3S Web Conf.
Volume 363, 2022
XV International Scientific Conference on Precision Agriculture and Agricultural Machinery Industry “State and Prospects for the Development of Agribusiness - INTERAGROMASH 2022”
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|---|---|---|
| Article Number | 01058 | |
| Number of page(s) | 8 | |
| Section | Sustainable Mobility and Logistics | |
| DOI | https://doi.org/10.1051/e3sconf/202236301058 | |
| Published online | 14 December 2022 | |
Analysis of solutions of a nonlinear system of differential equations with a small parameter
Moscow State University of Civil Engineering, 26, Yaroslavskoye shosse, Moscow, 129337, Russia
* Corresponding author: verapetelina51@gmail.com
Based on the results of the article, perturbations of the first and second order are determined in rectangular coordinates and components of the speed of the body. The constructed system of differential equations of the perturbed motion of the body makes it possible to create a unified algorithm for determining perturbations of the second and higher orders in the form of finite polynomials in powers of regularizing variables, which are selected at each stage of the approximation and with the help of approximating polynomials it is possible to calculate any intermediate point of the trajectory of the motion of the body. It was proved that the introduction of regularizing variables provides the representation of the right-hand sides of the system of differential equations of perturbed motion in the form of polynomials with respect to this regularizing variable. A procedure for reducing the degree of approximating polynomials using Chebyshev polynomials was also performed.
© The Authors, published by EDP Sciences, 2022
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