About choosing the form of perturbed body motion differential equations system

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. (paper)