Аналітичні Функції Нелінійних Параметрів Польоту Снаряда

Abstract

When calculating projectile flight trajectories, an urgent issue is the definition and representation of aerodynamic forces (moments) and parameters of the atmosphere, which are significantly non-linear in nature, in the system of mathematical models - differential equations of spatial motion of projectiles. A significant component of the error in determining the aerodynamic force is introduced by the operation of numerical differentiation of tabular values of aerodynamic coefficients, which are included as components in systems of differential equations. In this direction, a scientific approach based on the approximation of the data of aerodynamic coefficients and parameters of the atmosphere by analytical functions is promising, the requirement for which is the possibility of obtaining a single and continuous function within the entire range of changes in the flight parameters of the projectile and ensuring their best approximation to tabular data. A unified approach to the possibility of approximating qualitatively different aerodynamic coefficients and parameters of the atmosphere found further development; as approximating functions, it is proposed to use an analytical function as the sum of a reference function (error function) and a set of basic functions (Gaussian functions), which allows to obtain a continuous-differentiated approximating function on the segment of the change of the projectile flight parameter, which can be represented by a single analytical expression. The obtained values of the single continuous-differentiated on the segment of the change of the projectile flight parameter approximating the function of the aerodynamic coefficients and the parameters of the atmosphere, which are given by a single analytical expression, can be used to solve the problems of calculating Firing tables and preparing data using ballistic integrating algorithms for firing artillery systems. Keywords: aerodynamic forces (moments), parameters of the atmosphere, projectile, approximation, differentiation, analytical expression, error function, Gaussian function.