Mathematical modeling and computer simulation of a basic problem of tube artillery external ballistics by means of the Mathcad software

Abstract

The paper presents mathematical modeling and computer simulation (MM&CS) in the area of numerical solving of the basic problem of external ballistics for tubed artillery. Five-stage MM&CS scheme for conducting a ballistic simulation is developed. It is shown that a formal mathematical procedure allowing to solve the basic problem of external ballistics is a numerical solution of the Cauchy problem for a system of ballistic differential equations. The trajectory of a projectile flight for the 57-mm ZIS-2 anti-tank cannon is estimated. A solving algorithm and the Mathcad program code are given.The numerical solution for a system of four first order ballistic differential equations is a five-dimensional space.The possibility of visual presentation for a numerical solution was proposed in the form of a square matrix. The boundaries of each subspace are determined. A procedure based on spline functions is developed for checking the correctness of the numerical solution. As a result of such verification, the effects of a light increase in the error at the edges of the integration interval are observed. A comparison of the numerical solution of the basic ballistics problem is conducted by means of “soft“ and “stiff“ solver-functions.The trajectory parameters estimated by “soft“ and “stiff“ methods are the same up to the fifth decimal place.