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.