On the issue of load’s external ballistics under low-speed transportation

Purpose. Solution of the three-dimensional nonlinear problem of external ballistics and development of an approximate mathematical model of the dynamic process for cargo falling from low-speed aircraft, which makes it possible to obtain an analytical solution, which is possible in combination with a geometric representation of the dynamic process using computer algebra. Methodology. Utilizing a blend of analytical and numerical research algorithms, an innovative model was devised, grounded in a nonlinear system of differential equations characterized by time-varying coefficients. The applied three-dimensional approach to the dynamic problem with an initial velocity from a UAV, in the presence of frontal and side wind loading, made it possible to use the nonlinear theory of external ballistics. This streamlining of the problem involved solving a related system of differential equations with variable coefficients along corresponding coordinates, leveraging an asymptotic approach. Furthermore, the formulation of the problem incorporated applied mathematical analysis and modeling, accommodating various pertinent environmental parameters. Findings. The creation of mathematical models and algorithms for calculating the parameters of the dynamic process of falling loads from low-speed aircraft within the framework of the theory of nonlinear external ballistics is an urgent problem both from the point of view of the development of the dynamic theory of the specified class of systems, and the creation of effective calculation algorithms with the possibility of practical application. As a result of the research, characteristic valuations of the influence of variable coefficients on the results of estimated accuracy of landing as a derivative of time were obtained. The obtained analytical and graphical dependences with the provision of appropriate assessments of the applied approach make it possible to establish the correlation of methods and results. Originality. The relevance of scientific research in the field of nonlinear external ballistics is based both on the internal trends of the development of this science and on the urgent needs of modern industry. In this paper, an approximate analytical solution of the nonlinear problem of external ballistics is proposed, which is subject to the applied conditions of motion. The resulting dependencies made it possible to establish the relationship between the parameters and find the degree of their influence on the landing time function. Practical value. The derived analytical findings and solution methodology can be integrated into practical applications within the realms of mathematical physics and engineering computations. This is particularly pertinent in the advancement of control algorithms for ballistic systems.