Mathematical Model of Study the Aircraft Flight Trajectory

This work is devoted to the study of the unmanned aerial vehicle movement model. Attention is focused on the issue of studying the forces that determine the dynamics of movement, the resultant force is considered. Based on the fact that the equation of motion depends on the structural features and purpose of aircraft, and their arsenal is quite varied and multifaceted, the basis of the study is the tactical and technical characteristics (TSH) of operational-tactical missile systems. The model on the passive part of the trajectory, where the nature of the equation of motion is determined only by gravity and aerodynamic forces, is considered in the paper. Taking into account the maximum flight height and the probabilistic nature of errors in the calculations, it is proposed to consider the force of gravity as constant along the entire trajectory. Therefore, all efforts are directed at determining the numerical values for determining the aerodynamic force. TSH missiles are of great importance here. It is worth noting that there are no real and reliable data about the rocket, in particular its design and experimental data. They are either classified, or unreliable in advance (deliberately presented with some error), or are established experimentally with a certain degree of accuracy or probability. That is why the numerical values given in the paper should be taken as probabilistic. In the active part of the movement trajectory, the main attention is paid to determining the engine's thrust. The given numerical values characterizing its force, the tabulated experimental values are conditionally correct, but the errors are insignificant. Data on the natural forces of air movement are even more uncertain. This made it necessary to compare different types of rocket and determine «conditionally» correct values. Based on the proposed mathematical model, it is possible to solve the task of predicting the navigation of an unmanned aerial vehicle with the numerical values of its main characteristics and other necessary input data. This will make it possible to study and form optimization flight trajectories.