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

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.