Calculation of First-Order Perturbations at Body Motion by Analytical Method

Abstract

The article is concerned with representation of the first-order disturbances in the rectangular coordinates, which are components of regularized speed and motion time of an investigated body in the form of polynomials on degrees of a certain regularizing variable, the analysis of an arrangement and nature of singular points is carried out, possibility of representation of coordinates and components of motion speed in the form of polynomials is proved. The main result of the article is the development of the method for determining the first-order disturbances in the form of finite polynomials. This representation of rectangular coordinates, of the components of regularized speed was obtained through a series of successive replacements of the independent variable. An algorithm for calculating first-order disturbances in rectangular coordinates, which are components of the speed and time of body motion.