E3S Web Conf.
Volume 258, 2021Ural Environmental Science Forum “Sustainable Development of Industrial Region” (UESF-2021)
|Number of page(s)||8|
|Section||Energy Efficiency in Construction|
|Published online||20 May 2021|
Asymptotic approximation of the solution of a perturbed differential equation system
Moscow State University of Civil Engineering, 26, Yaroslavskoye shosse, 129337, Moscow, Russia
* Corresponding author: email@example.com
The article is devoted to the determination of second-order perturbations in rectangular coordinates and components of the body motion to be under study. The main difficulty in solving this problem was the choice of a system of differential equations of perturbed motion, the coefficients of the projections of the perturbing acceleration are entire functions with respect to the independent regularizing variable. This circumstance allows constructing a unified algorithm for determining perturbations of the second and higher order in the form of finite polynomials with respect to some regularizing variables that are selected at each stage of approximation. Special points are used to reduce the degree of approximating polynomials, as well as to choose regularizing variables. The problem of generation of an asymptotic approximation of the solution of a perturbed differential equation system is considered in the case where a bifurcation occurs in the “fast motions” equation when the parameter changes: two equilibrium positions merge, followed by a change in stability.
© The Authors, published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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