About choosing the form of perturbed body motion differential equations system

7th International Symposium Actual Problems of Computational Simulation in Civil Engineering

土木建筑工程;计算机科学

Petelina, V.D.^1

Department of Applied Mathematics, Moscow State University of Civil Engineering, 26, Yaroslavskoe shosse, Moscow

129337, Russia^1

关键词: Approximating polynomials;    Cartesian coordinate;    Higher-order perturbation;    Motion differential equation;    Motion trajectories;    Numerical integrations;    Rectangular coordinates;    Right-hand sides;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/456/1/012123/pdf
DOI  :  10.1088/1757-899X/456/1/012123

来源: IOP

【 摘 要 】

The article deals with determination of the second- and higher-order perturbations in Cartesian coordinates and body motion velocity constituents. A special perturbed motion differential equations system is constructed. The right-hand sides of this system are finite polynomials relative to an independent regularizing variable. This allows constructing a single algorithm to determine the second and higher order perturbations in the form of finite polynomials relative to some regularizing variables that are chosen at each approximation step. Following the calculations results with the use of the developed method, the coefficients of approximating polynomials representing rectangular coordinates and components of the regularized body speed were obtained. Comparison with the results of numerical integration of the equations of disturbed motion shows close agreement of the results. The developed methods make it possible to calculate, by the approximating polynomials, any intermediate point of the motion trajectory of the body.